Shared Concepts and Topics (Chapter) SAS/STAT

Shared Concepts and Topics (Chapter) SAS/STAT
®
SAS/STAT 12.3 User’s Guide
Shared Concepts and
Topics
(Chapter)
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Chapter 19
Shared Concepts and Topics
Contents
Levelization of Classification Variables . . . . . . . . . . . . . . . . . . . . . . . . . . . .
380
Parameterization of Model Effects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
383
GLM Parameterization of Classification Variables and Effects . . . . . . . . . . . . .
383
Intercept . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
383
Regression Effects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
383
Main Effects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
384
Interaction Effects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
384
Nested Effects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
385
Continuous-Nesting-Class Effects . . . . . . . . . . . . . . . . . . . . . . .
385
Continuous-by-Class Effects . . . . . . . . . . . . . . . . . . . . . . . . . .
386
General Effects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
386
Other Parameterizations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
387
CODE Statement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Syntax: CODE Statement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
390
391
EFFECT Statement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
393
Collection Effects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
395
Lag Effects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
395
Multimember Effects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
398
Polynomial Effects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
399
Spline Effects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
403
Splines and Spline Bases . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
406
Truncated Power Function Basis . . . . . . . . . . . . . . . . . . . . . . . .
407
B-Spline Basis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
408
Natural Cubic Spline Basis . . . . . . . . . . . . . . . . . . . . . . . . . . .
411
EFFECTPLOT Statement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
411
Syntax: EFFECTPLOT Statement . . . . . . . . . . . . . . . . . . . . . . . . . . . .
412
Dictionary of Options . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
414
ODS Graphics: EFFECTPLOT Statement . . . . . . . . . . . . . . . . . . . . . . . .
422
Examples: EFFECTPLOT Statement . . . . . . . . . . . . . . . . . . . . . . . . . .
423
Example 19.1: A Saddle Surface . . . . . . . . . . . . . . . . . . . . . . . . . . . .
423
Example 19.2: Unbalanced Two-Way ANOVA . . . . . . . . . . . . . . . . . . . . .
426
Example 19.3: Logistic Regression . . . . . . . . . . . . . . . . . . . . . . . . . . .
433
ESTIMATE Statement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
437
Syntax: ESTIMATE Statement . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
438
Positional and Nonpositional Syntax for Coefficients in Linear Functions . . . . . . .
448
380 F Chapter 19: Shared Concepts and Topics
Joint Hypothesis Tests with Complex Alternatives, the Chi-Bar-Square Statistic . . . .
451
ODS Table Names: ESTIMATE Statement . . . . . . . . . . . . . . . . . . . . . . .
452
ODS Graphics: ESTIMATE Statement . . . . . . . . . . . . . . . . . . . . . . . . .
452
LSMEANS Statement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
453
Syntax: LSMEANS Statement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
454
ODS Table Names: LSMEANS Statement . . . . . . . . . . . . . . . . . . . . . . .
468
ODS Graphics: LSMEANS Statement . . . . . . . . . . . . . . . . . . . . . . . . .
468
LSMESTIMATE Statement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
470
Syntax: LSMESTIMATE Statement . . . . . . . . . . . . . . . . . . . . . . . . . . .
471
ODS Table Names: LSMESTIMATE Statement . . . . . . . . . . . . . . . . . . . .
481
ODS Graphics: LSMESTIMATE Statement . . . . . . . . . . . . . . . . . . . . . . .
481
NLOPTIONS Statement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
482
Syntax: NLOPTIONS Statement . . . . . . . . . . . . . . . . . . . . . . . . . . . .
482
Choosing an Optimization Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . .
First- or Second-Order Algorithms . . . . . . . . . . . . . . . . . . . . . . .
494
494
Algorithm Descriptions . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
495
SLICE Statement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
498
Syntax: SLICE Statement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
500
ODS Table Names: SLICE Statement . . . . . . . . . . . . . . . . . . . . . . . . . .
501
STORE Statement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
501
Syntax: STORE Statement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
502
TEST Statement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
502
Syntax: TEST Statement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
503
ODS Table Names: TEST Statement . . . . . . . . . . . . . . . . . . . . . . . . . .
504
Programming Statements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
504
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
506
This chapter introduces a number of concepts that are common to two or more SAS/STAT procedures. Most
sections display a listing of the procedures for which the shared topic is relevant.
Levelization of Classification Variables
A classification variable is a variable that enters the statistical analysis or model not through its values, but
through its levels. The process of associating values of a variable with levels is termed levelization.
This section covers in particular procedures that support a CLASS statement for specifying classification
variables. Some of the concepts discussed also apply to procedures that use different syntax to request
levelization of variables (for example, the CLASS() transformation in the TRANSREG procedure).
During the process of levelization, observations that share the same value are assigned to the same level.
The manner in which values are grouped can be affected by the inclusion of formats. The sort order of
the levels can be determined with the ORDER= option in the procedure statement. With the GENMOD,
GLMSELECT, and LOGISTIC procedures, you can also control the sort order separately for each variable
in the CLASS statement.
Levelization of Classification Variables F 381
Consider the data on nine observations in Table 19.1. The variable A is integer valued, and the variable X
is a continuous variable with a missing value for the fourth observations. The fourth and fifth columns of
Table 19.1 apply two different formats to the variable X.
Table 19.1 Example Data for Levelization
Obs
A
x
FORMAT
x 3.0
FORMAT
x 3.1
1
2
3
4
5
6
7
8
9
2
2
2
3
3
3
4
4
4
1.09
1.13
1.27
.
2.26
2.48
3.34
3.34
3.14
1
1
1
.
2
2
3
3
3
1.1
1.1
1.3
.
2.3
2.5
3.3
3.3
3.1
By default, levelization of the variables groups observations by the formatted value of the variable, except
for numerical variables for which no explicit format is provided. Numerical variables for which no explicit
format is provided are sorted by their internal value. The levelization of the four columns in table Table 19.1
leads to the level assignment in Table 19.2.
Table 19.2 Values and Levels
Obs
A
Value Level
X
Value Level
FORMAT x 3.0
Value Level
FORMAT x 3.1
Value Level
1
2
3
4
5
6
7
8
9
2
2
2
3
3
3
4
4
4
1.09
1.13
1.27
.
2.26
2.48
3.34
3.34
3.14
1
1
1
.
2
2
3
3
3
1.1
1.1
1.3
.
2.3
2.5
3.3
3.3
3.1
1
1
1
2
2
2
3
3
3
1
2
3
.
4
5
7
7
6
1
1
1
.
2
2
3
3
3
1
1
2
.
3
4
6
6
5
The ORDER= option in the PROC statement specifies the sort order for the levels of CLASS variables.
When ORDER=FORMATTED (which is the default) is in effect for numeric variables for which you have
supplied no explicit format, the levels are ordered by their internal values. To order numeric class levels
with no explicit format by their BEST12. formatted values, you can specify the BEST12. format explicitly
for the CLASS variables.
The following table shows how values of the ORDER= option are interpreted.
382 F Chapter 19: Shared Concepts and Topics
Value of ORDER=
Levels Sorted By
DATA
Order of appearance in the input data set
FORMATTED
External formatted value, except for numeric variables
with no explicit format, which are sorted by their unformatted (internal) value
FREQ
Descending frequency count; levels with the most observations come first in the order
INTERNAL
Unformatted value
For FORMATTED and INTERNAL values, the sort order is machine dependent. For more information
about sort order, see the chapter on the SORT procedure in the Base SAS Procedures Guide and the discussion of BY-group processing in SAS Language Reference: Concepts.
The GLMSELECT, LOGISTIC, and GENMOD procedures support a MISSING option in the CLASS statement. When this option is in effect, missing values (‘.’ for a numeric variable and blanks for a character
variable) are included in the levelization and are assigned a level. Table 19.3 displays the results of levelizing
the values in Table 19.1 when the MISSING option is in effect.
Table 19.3 Values and Levels with MISSING Option
Obs
A
Value Level
X
Value Level
FORMAT x 3.0
Value Level
FORMAT x 3.1
Value Level
1
2
3
4
5
6
7
8
9
2
2
2
3
3
3
4
4
4
1.09
1.13
1.27
.
2.26
2.48
3.34
3.34
3.14
1
1
1
.
2
2
3
3
3
1.1
1.1
1.3
.
2.3
2.5
3.3
3.3
3.1
1
1
1
2
2
2
3
3
3
2
3
4
1
5
6
8
8
7
2
2
2
1
3
3
4
4
4
2
2
3
1
4
5
7
7
6
When the MISSING option is not specified, or for procedures whose CLASS statement does not support this
option, it is important to understand the implications of missing values for your statistical analysis. When
a SAS/STAT procedure levelizes the CLASS variables, an observation for which a CLASS variable has a
missing value is excluded from the analysis. This is true regardless of whether the variable is used to form
the statistical model. Consider, for example, the case where some observations contain missing values for
variable A but the records for these observations are otherwise complete with respect to all other variables
in the statistical models. The analysis results from the following statements do not include any observations
for which variable A contains missing values, even though A is not specified in the MODEL statement:
class A B;
model y = B x B*x;
Many statistical procedures print a “Number of Observations” table that shows the number of observations
read from the data set and the number of observations used in the analysis. Pay careful attention to this
Parameterization of Model Effects F 383
table—especially when your data set contains missing values—to ensure that no observations are unintentionally excluded from the analysis.
Parameterization of Model Effects
The general form of a linear regression model is defined in Chapter 3, “Regression Models and Models with
Classification Effects” as
Y D Xˇ C This section describes how matrices of regressor effects such as X are constructed in SAS/STAT software.
These constructions (parameterization rules) apply to regression models, models with classification effects,
generalized linear models, and mixed models. The simplest and most general parameterization rules are the
ones used in the GLM procedure, and they are discussed first. Several procedures also support alternate
parameterizations of classification variables, including the CATMOD, GENMOD, GLMSELECT, LOGISTIC, PHREG, SURVEYLOGISTIC, and SURVEYPHREG procedures. These are discussed after the GLM
parameterization of classification variables and model effects.
All modeling procedures that have a CLASS statement support classification variables and effects, and
those procedures that additionally support the supplemental parameterizations have a PARAM= option in
the CLASS statement.
GLM Parameterization of Classification Variables and Effects
This section applies to the following procedures:
GAM, GENMOD, GLIMMIX, GLM, GLMPOWER, GLMSELECT, LIFEREG, LOGISTIC, MI, MIXED,
MULLTEST, ORTHOREG, PHREG, PLS, QUANTREG, ROBUSTREG, SURVEYLOGISTIC, and SURVEYPHREG.
Intercept
By default, SAS/STAT linear models automatically include a column of 1s in X which corresponds to
an intercept parameter. In many procedures you can use the NOINT option in the MODEL statement to
suppress this intercept. For example, the NOINT option is useful when the MODEL statement contains a
classification effect and you want the parameter estimates to be in terms of the mean response for each level
of that effect.
Regression Effects
Numeric variables or polynomial terms that involve them can be included in the model as regression effects
(covariates). The actual values of such terms are included as columns of the relevant model matrices. You
can use the bar operator with a regression effect to generate polynomial effects. For example, X|X|X expands
to X X*X X*X*X, which is a cubic model.
384 F Chapter 19: Shared Concepts and Topics
Main Effects
If a classification variable has m levels, the GLM parameterization generates m columns for its main effect
in the model matrix. Each column is an indicator variable for a given level. The order of the columns is
the sort order of the values of their levels and frequently can be controlled with the ORDER= option in the
procedure or CLASS statement.
Table 19.4 is an example where ˇ0 denotes the intercept and A and B are classification variables with two
and three levels, respectively.
Table 19.4 Example of Main Effects
Data
A
B
1
1
1
2
2
2
1
2
3
1
2
3
I
A
ˇ0
1
1
1
1
1
1
A1
1
1
1
0
0
0
B
A2
0
0
0
1
1
1
B1
1
0
0
1
0
0
B2
0
1
0
0
1
0
B3
0
0
1
0
0
1
Typically, there are more columns for these effects than there are degrees of freedom to estimate them. In
other words, the GLM parameterization of main effects is singular.
Interaction Effects
Often a model includes interaction (crossed) effects to account for how the effect of a variable changes
with the values of other variables. With an interaction, the terms are first reordered to correspond to the
order of the variables in the CLASS statement. Thus, B*A becomes A*B if A precedes B in the CLASS
statement. Then, the GLM parameterization generates columns for all combinations of levels that occur in
the data. The order of the columns is such that the rightmost variables in the interaction change faster than
the leftmost variables (Table 19.5). In the MIXED and GLIMMIX procedures, which support both fixedand random-effects models, empty columns (that is, columns that would contain all 0s) are not generated
for fixed effects, but they are generated for random effects.
Table 19.5 Example of Interaction Effects
Data
A
B
1
1
1
2
2
2
1
2
3
1
2
3
I
ˇ0
1
1
1
1
1
1
A
A1
1
1
1
0
0
0
A*B
B
A2
0
0
0
1
1
1
B1
1
0
0
1
0
0
B2
0
1
0
0
1
0
B3
0
0
1
0
0
1
A1B1
1
0
0
0
0
0
A1B2
0
1
0
0
0
0
A1B3
0
0
1
0
0
0
A2B1
0
0
0
1
0
0
A2B2
0
0
0
0
1
0
A2B3
0
0
0
0
0
1
In the preceding matrix, main-effects columns are not linearly independent of crossed-effects columns; in
fact, the column space for the crossed effects contains the space of the main effect.
GLM Parameterization of Classification Variables and Effects F 385
When your model contains many interaction effects, you might be able to code them more parsimoniously
by using the bar operator ( | ). The bar operator generates all possible interaction effects. For example, A|B|C
expands to A B A*B C A*C B*C A*B*C. To eliminate higher-order interaction effects, use the at sign (@)
in conjunction with the bar operator. For instance, A|B|C|[email protected] expands to A B A*B C A*C B*C D A*D B*D
C*D.
Nested Effects
Nested effects are generated in the same manner as crossed effects. Hence, the design columns generated
by the following two statements are the same (but the ordering of the columns is different):
model Y=A B(A);
model Y=A A*B;
The nesting operator in SAS/STAT software is more of a notational convenience than an operation distinct
from crossing. Nested effects are typically characterized by the property that the nested variables never
appear as main effects. The order of the variables within nesting parentheses is made to correspond to the
order of these variables in the CLASS statement. The order of the columns is such that variables outside the
parentheses index faster than those inside the parentheses, and the rightmost nested variables index faster
than the leftmost variables (Table 19.6).
Table 19.6 Example of Nested Effects
Data
A
B
1
1
1
2
2
2
1
2
3
1
2
3
I
B(A)
A
ˇ0
1
1
1
1
1
1
A1
1
1
1
0
0
0
A2
0
0
0
1
1
1
B1A1
1
0
0
0
0
0
B2A1
0
1
0
0
0
0
B3A1
0
0
1
0
0
0
B1A2
0
0
0
1
0
0
B2A2
0
0
0
0
1
0
B3A2
0
0
0
0
0
1
Continuous-Nesting-Class Effects
When a continuous variable nests or crosses with a classification variable, the design columns are constructed by multiplying the continuous values into the design columns for the classification effect (Table 19.7).
Table 19.7 Example of Continuous-Nesting-Class Effects
Data
X
A
21
24
22
28
19
23
1
1
1
2
2
2
I
ˇ0
1
1
1
1
1
1
X(A)
A
A1
1
1
1
0
0
0
A2
0
0
0
1
1
1
X(A1)
21
24
22
0
0
0
X(A2)
0
0
0
28
19
23
386 F Chapter 19: Shared Concepts and Topics
This model estimates a separate intercept and a separate slope for X within each level of A.
Continuous-by-Class Effects
Continuous-by-class effects generate the same design columns as continuous-nesting-class effects. Table 19.8 shows the construction of the X*A effect. The two columns for this effect are the same as the
columns for the X(A) effect in Table 19.7.
Table 19.8 Example of Continuous-by-Class Effects
Data
X
A
21
24
22
28
19
23
1
1
1
2
2
2
I
X
ˇ0
1
1
1
1
1
1
X
21
24
22
28
19
23
X *A
A
A1
1
1
1
0
0
0
A2
0
0
0
1
1
1
X*A1
21
24
22
0
0
0
X*A2
0
0
0
28
19
23
You can use continuous-by-class effects together with pure continuous effects to test for homogeneity of
slopes.
General Effects
An example that combines all the effects is X1*X2*A*B*C(D E). The continuous list comes first, followed
by the crossed list, followed by the nested list in parentheses. You should be aware of the sequencing of
parameters when you use statements that depend on the ordering of parameters. Such statements include
CONTRAST and ESTIMATE statements, which are used in a number of procedures to estimate and test
functions of the parameters.
Effects might be renamed by the procedure to correspond to ordering rules. For example, B*A(E D) might
be renamed A*B(D E) to satisfy the following:
Classification variables that occur outside parentheses (crossed effects) are sorted in the order in which
they appear in the CLASS statement.
Variables within parentheses (nested effects) are sorted in the order in which they appear in the CLASS
statement.
The sequencing of the parameters generated by an effect can be described by which variables have their
levels indexed faster:
Variables in the crossed list index faster than variables in the nested list.
Within a crossed or nested list, variables to the right index faster than variables to the left.
For example, suppose a model includes four effects—A, B, C, and D—each having two levels, 1 and 2. If
the CLASS statement is
Other Parameterizations F 387
class A B C D;
then the order
A*B(C D), is
A1 B1 C1 D1
A1 B1 C1 D2
A1 B1 C2 D1
A1 B1 C2 D2
!
!
!
!
of
the
parameters
A1 B2 C1 D1
A1 B2 C1 D2
A1 B2 C2 D1
A1 B2 C2 D2
!
!
!
!
for
A2 B1 C1 D1
A2 B1 C1 D2
A2 B1 C2 D1
A2 B1 C2 D2
the
effect
B*A(C
D),
which
is
renamed
! A2 B2 C1 D1 !
! A2 B2 C1 D2 !
! A2 B2 C2 D1 !
! A2 B2 C2 D2
Note that first the crossed effects B and A are sorted in the order in which they appear in the CLASS
statement so that A precedes B in the parameter list. Then, for each combination of the nested effects in
turn, combinations of A and B appear. The B effect changes fastest because it is rightmost in the cross list.
Then A changes next fastest, and D changes next fastest. The C effect changes most slowly because it is
leftmost in the nested list.
Other Parameterizations
This section applies to the following procedures:
CATMOD, GENMOD, GLMSELECT, LOGISTIC, PHREG, and SURVEYPHREG.
Some SAS/STAT procedures, including GENMOD, GLMSELECT, and LOGISTIC, support nonsingular
parameterizations for classification effects. A variety of these nonsingular parameterizations are available.
In most of these procedures you use the PARAM= option in the CLASS statement to specify the parameterization.
Consider a model with one CLASS variable A that has four levels, 1, 2, 5, and 7. Details of the possible
choices for the PARAM= option follow.
EFFECT
Three columns are created to indicate group membership of the nonreference levels.
For the reference level, all three dummy variables have a value of –1. For example,
if the reference level is 7 (REF=7), the design matrix columns for A are as follows.
Effect Coding
A
Design Matrix
A1 A2 A5
1
2
5
7
1
0
0
–1
0
1
0
–1
0
0
1
–1
Parameter estimates of CLASS main effects that use the effect coding scheme estimate the difference in the effect of each nonreference level compared to the average
effect over all four levels.
388 F Chapter 19: Shared Concepts and Topics
The EFFECT parameterization is the default parameterization in the CATMOD procedure. See the section “Generation of the Design Matrix” on page 1832, in Chapter 30, “The CATMOD Procedure,” for further details about parameterization of
model effects with the CATMOD procedure.
GLM
As in the GLM procedure, four columns are created to indicate group membership.
The design matrix columns for A are as follows.
GLM Coding
A
1
2
5
7
Design Matrix
A1 A2 A5 A7
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
Parameter estimates of CLASS main effects that use the GLM coding scheme estimate the difference in the effects of each level compared to the last level. See the
previous section for details about the GLM parameterization of model effects.
ORDINAL | THERMOMETER Three columns are created to indicate group membership of the higher
levels of the effect. For the first level of the effect (which for A is 1), all three
dummy variables have a value of 0. The design matrix columns for A are as follows.
Ordinal Coding
A
1
2
5
7
Design Matrix
A2 A5 A7
0
1
1
1
0
0
1
1
0
0
0
1
The first level of the effect is a control or baseline level. Parameter estimates of
CLASS main effects, using the ORDINAL coding scheme, estimate the differences
between effects of successive levels. When the parameters have the same sign, the
effect is monotonic across the levels.
POLYNOMIAL | POLY Three columns are created. The
first represents the linear term .x/, the second
2
represents the quadratic term x , and the third represents the cubic term x 3 ,
where x is the level value. If the CLASS levels are not numeric, they are translated
into 1, 2, 3, : : : according to their sort order. The design matrix columns for A are as
follows.
Other Parameterizations F 389
Polynomial Coding
A
Design Matrix
APOLY1 APOLY2 APOLY3
1
2
5
7
REFERENCE | REF
1
2
5
7
1
4
25
49
1
8
125
343
Three columns are created to indicate group membership of the nonreference levels.
For the reference level, all three dummy variables have a value of 0. For example, if
the reference level is 7 (REF=7), the design matrix columns for A are as follows.
Reference Coding
A
1
2
5
7
Design Matrix
A1 A2 A5
1
0
0
0
0
1
0
0
0
0
1
0
Parameter estimates of CLASS main effects that use the reference coding scheme
estimate the difference in the effect of each nonreference level compared to the effect
of the reference level.
The REFERENCE parameterization is also available through the MODEL statement
in the CATMOD procedure. See the section “Generation of the Design Matrix”
on page 1832, in Chapter 30, “The CATMOD Procedure,” for further details about
parameterization of model effects with the CATMOD procedure.
ORTHEFFECT
The columns are obtained by applying the Gram-Schmidt orthogonalization to the
columns for PARAM=EFFECT. The design matrix columns for A are as follows.
Orthogonal Effect Coding
A
Design Matrix
AOEFF1 AOEFF2 AOEFF3
1
2
5
7
1.41421
0
0
–1.41421
–0.81650
1.63299
0
–0.81649
–0.57735
–0.57735
1.73205
–0.57735
ORTHORDINAL | ORTHOTHERM The columns are obtained by applying the Gram-Schmidt orthogonalization to the columns for PARAM=ORDINAL. The design matrix columns for
A are as follows.
390 F Chapter 19: Shared Concepts and Topics
Orthogonal Ordinal Coding
A
1
2
5
7
ORTHPOLY
Design Matrix
AOORD1 AOORD2 AOORD3
–1.73205
0.57735
0.57735
0.57735
0
–1.63299
0.81650
0.81650
0
0
–1.41421
1.41421
The columns are obtained by applying the Gram-Schmidt orthogonalization to the
columns for PARAM=POLY. The design matrix columns for A are as follows.
Orthogonal Polynomial Coding
A
1
2
5
7
ORTHREF
Design Matrix
AOPOLY1 AOPOLY2 AOPOLY5
–1.15311
–0.73380
0.52414
1.36277
0.90712
–0.54041
–1.37034
1.00363
–0.92058
1.47292
–0.92058
0.36823
The columns are obtained by applying the Gram-Schmidt orthogonalization to the
columns for PARAM=REFERENCE. The design matrix columns for A are as follows.
Orthogonal Reference Coding
A
AOREF1
1
2
5
7
1.73205
–0.57735
–0.57735
–0.57735
Design Matrix
AOREF2 AOREF3
0
1.63299
–0.81650
–0.81650
0
0
1.41421
–1.41421
CODE Statement
This statement documentation applies to the following procedures:
GENMOD, GLIMMIX, GLM, GLMSELECT, LOGISTIC, MIXED, PLM, and REG. It also applies to the
HPLOGISTIC and HPREG procedures in SAS High-Performance Analytics software.
The CODE statement enables you to write SAS DATA step code to a file or catalog entry for computing
predicted values of the fitted model. This code can then be included in a DATA step to score new data.
For example, in the following program, the CODE statement writes the code for predicting the outcome
of a logistic model to the file mycode.sas. The file is subsequently included in a DATA step to score the
sashelp.Bmt data.
Syntax: CODE Statement F 391
proc logistic data=sashelp.Bmt;
class Group;
model Status=Group;
code file='mycode.sas';
run;
data Score;
set sashelp.Bmt;
%include mycode;
run;
Syntax: CODE Statement
CODE < options > ;
Table 19.9 summarizes the options you can specify in the CODE statement.
Table 19.9 CODE Statement Options
Option
Description
CATALOG=
DUMMIES
ERROR
FILE=
FORMAT=
GROUP=
IMPUTE
Names the catalog entry where the generated code is saved
Retains the dummy variables in the data set
Computes the error function
Names the file where the generated code is saved
Specifies the numeric format for the regression coefficients
Specifies the group identifier for array names and statement labels
Imputes predicted values for observations with missing or invalid
covariates
Specifies the line size of the generated code
Specifies the algorithm for looking up CLASS levels
Computes residuals
LINESIZE=
LOOKUP=
RESIDUAL
You cannot specify both the FILE= and CATALOG= options. If you specify neither, the SAS scoring code
is written to the SAS log. You can specify the following options in the CODE statement.
CATALOG=library.catalog.entry.type
CAT=library.catalog.entry.type
specifies where to write the generated code in the form of library.catalog.entry.type. The compound
name can have from one to four levels. The default library is determined by the USER= SAS system
option, which by default is WORK. The default entry is SASCODE, and the default type is SOURCE.
DUMMIES | NODUMMIES
specifies whether to keep dummy variables that represent the CLASS levels in the data set. The
default is NODUMMIES, which specifies that dummy variables not be retained.
392 F Chapter 19: Shared Concepts and Topics
ERROR | NOERROR
specifies whether to generate code to compute the error function. The default is NOERROR, which
specifies that the error function not be generated.
FILE=filename
names the external file that saves the generated code. When enclosed in a quoted string (for example,
FILE="c:nmydirnscorecode.sas"), this option specifies the path for writing the code to an external
file. You can also specify unquoted SAS filenames of no more than eight characters for filename. If
the filename is assigned as a fileref in a Base SAS FILENAME statement, the file specified in the
FILENAME statement is opened. The special filerefs LOG and PRINT are always assigned. If the
specified filename is not an assigned fileref, the specified value for filename is concatenated with a .txt
extension before the file is opened. For example, if FOO is not an assigned fileref, FILE=FOO causes
FOO.txt to be opened. If filename has more than eight characters, an error message is printed.
FORMAT=format
specifies the format for the regression coefficients and other numerical values that do not have a format
from the input data set. The default format is BEST20.
GROUP=group-name
specifies the group identifier for group processing. The group-name should be a valid SAS name of
no more than 16 characters. It is used to construct array names and statement labels in the generated
code.
IMPUTE
imputes the predicted values according to an intercept-only model for observations with missing or
invalid covariate values. For a continuous response, the predicted value is the mean of the response
variable; for a categorical response, the predicted values are the proportions of the response categories.
When the IMPUTE option is specified, the scoring code also creates a variable named _WARN_ that
contains one or more single-character codes that indicate problems in computing predicted values.
The character codes used in _WARN_ go in the following positions:
Table 19.10 _WARN_ Variable Codes
Code
M
U
Column
1
2
Meaning
Missing covariate value
Unrecognized covariate category
LINESIZE=value
LS=value
specifies the line size for the generated code. The default is 72. The permissible range is 64 to 254.
LOOKUP=lookup-method
specifies the algorithm for looking up CLASS levels. You can specify the following lookup-methods:
AUTO
selects the LINEAR algorithm if a CLASS variable has fewer than five categories; otherwise,
the BINARY algorithm is used. This is the default.
EFFECT Statement F 393
BINARY
uses a binary search. This method is fast, but might produce incorrect results and the normalized
category values might contain characters that collate in different orders in ASCII and EBCDIC,
if you generate the code on an ASCII machine and execute the code on an EBCDIC machine or
vice versa.
LINEAR
uses a linear search with IF statements that have categories in the order of the class levels. This
method is slow if there are many categories.
SELECT
uses a SELECT statement.
The default is LOOKUP=AUTO.
RESIDUAL | NORESIDUAL
specifies whether to generate code to compute residual values. If you request code for residuals and
then score a data set that does not contain target values, the residuals will have missing values. The
default is NORESIDUAL, which specifies that the code for residuals not be generated.
EFFECT Statement
This section applies to the following procedures:
GLIMMIX, GLMSELECT, HPMIXED, LOGISTIC, ORTHOREG, PHREG, PLS, QUANTLIFE,
QUANTREG, QUANTSELECT, ROBUSTREG, SURVEYLOGISTIC, and SURVEYREG.
The EFFECT statement enables you to construct special collections of columns for design matrices. These
collections are referred to as constructed effects to distinguish them from the usual model effects that are
formed from continuous or classification variables, as discussed in the section “GLM Parameterization of
Classification Variables and Effects” on page 383. For example, the terms A, B, x, A*x, A*B, and sub in the
following statements define fixed, random, and subject effects of the usual type in a mixed model:
proc glimmix;
class A B sub;
model y = A B x A*x;
random A*B / subject=sub;
run;
A constructed effect, on the other hand, is assigned through the EFFECT statement. For example, in the
following program, the EFFECT statement defines a constructed effect named spl:
proc glimmix;
class A B SUB;
effect spl = spline(x);
model y = A B A*spl;
random A*B / subject=sub;
run;
394 F Chapter 19: Shared Concepts and Topics
The columns of spl are formed from the data set variable x as a cubic B-spline basis with three equally
spaced interior knots.
Each constructed effect corresponds to a collection of columns that are referred to by using the name
you supply. You can specify multiple EFFECT statements, and all EFFECT statements must precede the
MODEL statement.
The general syntax for the EFFECT statement with effect-specification is
EFFECT effect-name = effect-type (var-list < / effect-options >) ;
The name of the effect is specified after the EFFECT keyword. This name can appear in only one EFFECT
statement and cannot be the name of a variable in the input data set. The effect-type is specified after an
equal sign, followed by a list of variables within parentheses which are used in constructing the effect.
Effect-options that are specific to an effect-type can be specified after a slash (/) following the variable list.
The following effect-types are available and are discussed in the following sections:
COLLECTION
is a collection effect that defines one or more variables as a single effect with
multiple degrees of freedom. The variables in a collection are considered as
a unit for estimation and inference.
LAG
is a classification effect in which the level that is used for a given period
corresponds to the level in the preceding period.
MULTIMEMBER | MM
is a multimember classification effect whose levels are determined by one or
more variables that appear in a CLASS statement.
POLYNOMIAL | POLY
is a multivariate polynomial effect in the specified numeric variables.
SPLINE
is a regression spline effect whose columns are univariate spline expansions
of one or more variables. A spline expansion replaces the original variable
with an expanded or larger set of new variables.
Table 19.11 summarizes the options available in the EFFECT statement.
Table 19.11
Option
EFFECT Statement Options
Description
Collection Effects Options
DETAILS
Displays the constituents of the collection effect
Lag Effects Options
DESIGNROLE=
Names a variable that controls to which lag design an observation
is assigned
DETAILS
Displays the lag design of the lag effect
NLAG=
Specifies the number of periods in the lag
PERIOD=
Names the variable that defines the period
WITHIN=
Names the variable or variables that define the group within which
each period is defined
Collection Effects F 395
Table 19.11 continued
Option
Description
Multimember Effects Options
NOEFFECT
Specifies that observations with all missing levels for the multimember variables should have zero values in the corresponding
design matrix columns
WEIGHT=
Specifies the weight variable for the contributions of each of the
classification effects
Polynomial Effects Options
DEGREE=
Specifies the degree of the polynomial
MDEGREE=
Specifies the maximum degree of any variable in a term of the
polynomial
STANDARDIZE=
Specifies centering and scaling suboptions for the variables that
define the polynomial
Spline Effects Options
BASIS=
DEGREE=
KNOTMETHOD=
Specifies the type of basis (B-spline basis or truncated power function basis) for the spline expansion
Specifies the degree of the spline transformation
Specifies how to construct the knots for spline effects
Collection Effects
EFFECT name=COLLECTION (var-list < / DETAILS >) ;
You use a collection effect to define a set of variables that are treated as a single effect with multiple degrees
of freedom. The variables in var-list can be continuous or classification variables. The columns in the design
matrix that are contributed by a collection effect are the design columns of its constituent variables in the
order in which they appear in the definition of the collection effect. If you specify the DETAILS option,
then a table that shows the constituents of the collection effect is displayed.
Lag Effects
EFFECT name=LAG (variable / lag-options) ;
A lag effect is a classification effect for the CLASS variable that is given after the keyword LAG. A lag
effect is used to represent the effect of a previous value of the lagged variable when there is some inherent
ordering of the observations of this variable. A typical example where lag effects are useful is a study in
which different subjects are given sequences of treatments and you want to investigate whether the treatment
in the previous period is important in understanding the outcome in the current period. You can do this by
including a lagged treatment effect in your model.
The precise definition of a LAG effect depends on a subdivision of the data into disjoint subsets, often
referred to as “subjects,” and an ordering into units called “periods” of the observations within a subject.
396 F Chapter 19: Shared Concepts and Topics
For an observation that belongs to a given subject and at a given period, the design matrix columns of
the lagged variable are the usual design matrix columns of that variable except for the observation at the
preceding period for that subject. Observations at the initial period do not have a preceding value, and so
the design matrix columns of the lag effect for these observations are set to zero. You can also define lag
effects where the number of periods that are lagged is greater than one. If the number of periods that are
lagged is n, then the design matrix columns of observations in periods less than or equal to n are set to zero.
The design matrix columns that correspond to a subject at period p, where p > n, are the usual design matrix
columns of the lagged variable for that subject at period p – n.
A convenient way to represent the organization of observations into subjects and periods is to form the lag
design matrix. The rows and columns of this matrix correspond to the subjects and periods respectively.
The lag design matrix entry is the treatment for the corresponding subject and period. In a valid lag design
there is at most one observation for a given period and subject. For example, the following set of treatments
by subject and period form a valid lag design:
Subject
Period
Sheila
Joey
Athena
Gelindo
Sheila
Joey
Athena
Gelindo
Sheila
Joey
Athena
Gelindo
Treatment
1
1
1
1
2
2
2
2
3
3
3
3
B
A
A
A
C
A
.
B
B
C
A
B
The associated lag design matrix is
Subject
--Period--1
2
3
Athena
Gelindo
Joey
Sheila
A
A
A
B
B
A
C
A
B
C
B
Note that the subject Athena did not receive a treatment at period 2, and so the corresponding entry in the
lag design matrix is missing. You can define a lag effect for this lag design with the following statements:
CLASS treatment;
EFFECT Lag = LAG( treatment / WITHIN=subject PERIOD=period);
When GLM coding is used for the CLASS variable treatment, the design matrix columns Lag_A, Lag_B,
and Lag_C for the constructed effect Lag are as follows:
Lag Effects F 397
Subject
period
Athena
Athena
Athena
Gelindo
Gelindo
Gelindo
Joey
Joey
Joey
Sheila
Sheila
Sheila
1
2
3
1
2
3
1
2
3
1
2
3
treatment
Lag_A
Lag_B
Lag_C
A
0
1
.
0
1
0
0
1
1
0
0
0
0
0
.
0
0
1
0
0
0
0
1
0
0
0
.
0
0
0
0
0
0
0
0
1
A
A
B
B
A
A
C
B
C
B
The design matrix columns for each subject at period 1 are all zero because there are no lagged observations
for period 1. You can also see that the design matrix columns at period 3 for subject Athena are missing
because Athena did not receive a treatment at period 2. Nevertheless, the design matrix columns for Athena
at period 2 are nonmissing and correspond to the treatment “A” that she received in period 1.
The following lag-options are required:
PERIOD=variable
specifies the period variable of the LAG design. The number of periods is the number of unique
formatted values of the PERIOD= variable, and the ordering of the period is formed by sorting these
formatted values in ascending order. You must specify a PERIOD= variable.
WITHIN=(variables)
WITHIN=variable
specifies a variable (or a list of variables within parentheses) that defines the subject grouping of the
lag design. If there is only one WITHIN= variable, then the parentheses are not required. Each subject
is defined by the unique set of formatted values of the variables in the WITHIN= list. The subjects
are sorted in ascending lexicographic order. You must specify a WITHIN= variable.
You can also specify the following lag-options:
DESIGNROLE=variable
specifies a numeric variable that is used to subset observations into a fitting group in which the value
of the DESIGNROLE= variable is nonzero and a second group in which the value of the specified
variable is zero. The observations in the fitting group are used to form the LAG design matrix that
is used in fitting the model. The LAG design that corresponds to the non-fitting group is used when
scoring observations in the input data set that do not belong to the fitting group. This option is useful
when you want to obtain predicted values in an output data set for observations that are not used in
fitting the model. If you do not specify a DESIGNROLE= variable, then all observations are assigned
to the fitting group.
DETAILS
requests a table that shows the lag design matrix of the lag effect.
398 F Chapter 19: Shared Concepts and Topics
NLAG= n
specifies the number of lags. By default NLAG=1.
Multimember Effects
EFFECT name=MULTIMEMBER (var-list < / mm-options >) ;
EFFECT name=MM (var-list < / mm-options >) ;
A multimember effect is formed from one or more classification variables in such a way that each observation can be associated with one or more levels of the union of the levels of the classification variables. In
other words, a multimember effect is a classification-type effect with possibly more than one nonzero column entry for each observation. Multimember effects are useful, for example, in modeling the following:
nurses’ effects on patient recovery in hospitals
teachers’ effects on student scores
lineage effects in genetic studies. See Example 41.16 in Chapter 41, “The GLIMMIX Procedure,”
for an application with random multimember effects in a genetic diallel experiment.
The levels of a multimember effect consist of the union of formatted values of the variables that define this
effect. Each such level contributes one column to the design matrix. For each observation, the value that
corresponds to each level of the multimember effect in the design matrix is the number of times that this
level occurs for the observation.
For example, the following data provide teacher information and end-of-year test scores for students after
two semesters:
Student
Score
Mary
Tom
Fred
Jane
Jack
87
89
82
88
99
Teacher1
Teacher2
Tobias
Rodriguez
Cohen
Tobias
.
Cohen
Tobias
Cohen
.
.
For example, Mary had different teachers in the two semesters, Fred had the same teacher in both semesters,
and Jane received instruction only in the first semester.
You can model the effect of the teachers on student performance by using a multimember effect specified as
follows:
CLASS teacher1 teacher2;
EFFECT teacher = MM(teacher1 teacher2);
The levels of the teacher effect are Cohen, Rodriguez, and Tobias, and the associated design matrix columns
are as follows:
Polynomial Effects F 399
Student
Cohen
Rodriguez
Mary
Tom
Fred
Jane
Jack
1
0
2
0
.
0
1
0
0
.
Tobias
1
1
0
1
.
You can specify the following mm-options after a slash (/):
DETAILS
requests a table that shows the levels of the multimember effect.
NOEFFECT
specifies that, for observations with all missing levels of the multimember variables, the values in the
corresponding design matrix columns be set to zero. If, in the preceding example, the teacher effect
is defined by
EFFECT teacher = MM(teacher1 teacher2 / noeffect);
then the associated design matrix columns values for Jack are all zero. This enables you to include
Jack in the analysis even though there is no effect of teachers on his performance.
A situation where it is important to designate observations as having no effect due to a classification
variable is the analysis of crossover designs, where lagged treatment levels are used to model the
carryover effects of treatments between periods. Since there is no carryover effect for the first period,
the treatment lag effect in a crossover design can be modeled with a multimember effect that consists
of a single classification variable and the NOEFFECT option, as in the following statements:
CLASS Treatment lagTreatment;
EFFECT Carryover = MM(lagTreatment / noeffect);
The lagTreatment variable contains a missing value for the first period. Otherwise, it contains the
value of the treatment variable for the preceding period.
STDIZE
specifies that for each observation, the entries in the design matrix that corresponds to the multimember effect be scaled to have a sum of one.
WEIGHT=wght-list
specifies numeric variables used to weigh the contributions of each of the classification effects that
define the constructed multimember effect. The number of variables in wght-list must match the
number of classification variables that define the effect.
Polynomial Effects
EFFECT name=POLYNOMIAL (var-list < / polynomial-options >) ;
EFFECT name=POLY (var-list < / polynomial-options >) ;
400 F Chapter 19: Shared Concepts and Topics
The variables in var-list must be numeric. A design matrix column is generated for each term of the specified
polynomial. By default, each of these terms is treated as a separate effect for the purpose of model building.
For example, the statements
proc glmselect;
effect MyPoly = polynomial(x1-x3/degree=2);
model y = MyPoly;
run;
yield the identical analysis to the statements
proc glmselect;
model y = x1 x2 x3 x1*x1 x1*x2 x1*x3 x2*x2 x2*x3 x3*x3;
run;
You can specify the following polynomial-options after a slash (/):
DEGREE=n
specifies the degree of the polynomial. The degree must be a positive integer. The degree is typically
a small integer, such as 1, 2, or 3. The default is DEGREE=1.
DETAILS
requests a table that shows the details of the specified polynomial, including the number of terms
generated. If you also specify the STANDARDIZE option, then a table that shows the standardization
details is also produced.
LABELSTYLE=(style-opts)
LABELSTYLE=style-opt
specifies how the terms in the polynomial are labeled. By default, powers are shown with ˆ as the
exponentiation operator and * as the multiplication operator. For example, a polynomial term such
as x13 x2 x32 is labeled x1ˆ3*x2*x3ˆ2. You can change the style of the label by using the following
style-opts within parentheses. If you specify a single style-opt, then you can omit the enclosing
parentheses.
EXPAND
specifies that each variable with an exponent greater than 1 be written as products of that variable. For example, the term x13 x2 x32 receives the label x1*x1*x1*x2*x3*x3.
EXPONENT < =quoted string >
specifies that each variable with an exponent greater than 1 be written using exponential notation.
By default, the symbol ˆ is used as the exponentiation operator. If you supply the optional quoted
string after an equal sign, then that string is used as the exponentiation operator. For example, if
you specify
LABELSTYLE=(EXPONENT="**")
then the term x13 x2 x32 receives the label x1**3*x2*x3**2.
INCLUDENAME
specifies that the name of the effect followed by an underscore be used as a prefix for term labels.
For example, the following statement generates terms with labels MyPoly_x1 and MyPoly_x1ˆ2:
Polynomial Effects F 401
EFFECT MyPoly=POLYNOMIAL(x1/degree=2 labelstyle=INCLUDENAME)
The INCLUDENAME option is ignored if you also specify the NOSEPARATE option in the
EFFECT=POLYNOMIAL statement.
PRODUCTSYMBOL=NONE | quoted string
specifies that the supplied string be used as the product symbol. For example, the following
statement generates terms with labels x1, x2, and x1 x2:
EFFECT MyPoly=POLYNOMIAL(x1 x2 / degree=2 mdegree=1
labelstyle=(PRODUCTSYMBOL=" "))
If you specify PRODUCTSYMBOL=NONE, then the labels are formed by juxtaposing the constituent variable names.
MDEGREE=n
specifies the maximum degree of any variable in a term of the polynomial. This degree must be a
positive integer. The default is the degree of the specified polynomial. For example, the following
statement generates the terms x1 , x2 , x12 , x1 x2 , x22 , x12 x2 , x1 x22 and x12 x22 :
EFFECT MyPoly=POLYNOMIAL(x1 x2/degree=4 MDEGREE=2);
NOSEPARATE
specifies that the polynomial be treated as a single effect with multiple degrees of freedom. The effect
name that you specify is used as the constructed effect name, and the labels of the terms are used as
labels of the corresponding parameters.
STANDARDIZE < (centerscale-opts) > < = standardize-opt >
specifies that the variables that define the polynomial be standardized. By default, the standardized
variables receive prefix “s_” in the variable names.
You can use the following centerscale-opts to specify how the center and scale are estimated:
METHOD=MOMENTS
specifies that the center be estimated by the variable mean and the scale be estimated by the
standard deviation. If a weight variable is specified using a WEIGHT statement, the observations
with invalid weights are ignored when forming the mean and standard deviation, but the weights
are otherwise not used. Only observations that are used in performing the analysis are used for
the standardization.
METHOD=RANGE
specifies that the center be estimated by the midpoint of the variable range and the scale be
estimated as half the variable range. Any observation that has a missing value for any regressor
used in the model is ignored when computing the range of variables in a polynomial effect.
Observations with valid regressor values but missing or invalid values of frequency variables,
weight variables, or dependent variables are used in computing variable ranges. The default (if
you do not specify the METHOD= suboption) is METHOD=RANGE.
402 F Chapter 19: Shared Concepts and Topics
METHOD=WMOMENTS
is the same as METHOD=MOMENTS except that weighted means and weighted standard deviations are used.
Let
n D number of observations used in the analysis
w D weight variable
f
D frequency variable
x D variable to be standardized
x.n/ D MaxniD1 .xi /
x.1/ D MinniD1 .xi /
F
D sum of frequencies
D †niD1 fi
WF D sum of weighted frequencies
D †niD1 wi fi
Table 19.12 shows how the center and scale are computed for each of the supported methods.
Table 19.12 Center and Scale Estimates by Method
Method
Center
Scale
Range
.x.n/ C x.1/ /=2
Moments
xN D †niD1 fi xi =F
WMoments
xN w D †niD1 wi fi xi =WF
.x.n/ x.1/ /=2
q
†n fi .xi x/
N 2 =.F 1/
q i D1
†niD1 wi fi .xi xN w /2 =.F 1/
PREFIX=NONE | quoted-string
specifies the prefix that is appended to standardized variables when forming the term labels. If
you omit this option, the default prefix is “s_”. If you specify PREFIX=NONE, then standardized variables are not prefixed.
You can control whether the standardization is to center, scale, or both center and scale by specifying
a standardize-opt:
CENTER
specifies that variables be centered but not scaled. For a variable x,
s_x D x
center
Spline Effects F 403
CENTERSCALE
specifies that variables be centered and scaled. This is the default if you do not specify a
standardization-opt. For a variable x,
s_x D
x
center
scale
NONE
specifies that no standardization be performed.
SCALE
specifies that variables be scaled but not centered. For a variable x,
s_x D
x
scale
Spline Effects
This section discusses the construction of spline effects through the EFFECT statement. You can also
include spline effects in statistical models by other means. The TRANSREG procedure has dedicated
facilities for including regression splines in your model and controlling the construction of the splines. For
example, you can use the TRANSREG procedure to fit a spline function but restrict the function to be
always increasing or decreasing (monotone). See the section “Using Splines and Knots” on page 8233 in
Chapter 97, “The TRANSREG Procedure,” for more information about using splines with the TRANSREG
procedure. The GAM and TPSPLINE procedures also can model the effects of regressor variables in terms
of smooth functions that are generated from spline bases. For more information see Chapter 39, “The GAM
Procedure,” and Chapter 96, “The TPSPLINE Procedure.”
A spline effect expands variables into spline bases whose form depends on the options that you specify.
You can find details about regression splines and spline bases in the section “Splines and Spline Bases” on
page 406. You request a spline effect with the syntax
EFFECT name=SPLINE (var-list < / spline-options >) ;
The variables in var-list must be numeric. Design matrix columns are generated separately for each of these
variables, and the set of columns is collectively referred to with the specified name. By default, the spline
basis that is generated for each variable is a cubic B-spline basis with three equally spaced knots positioned
between the minimum and maximum values of that variable. This yields by default seven design matrix
columns for each of the variables in the SPLINE effect.
You can specify the following spline-options after a slash (/):
BASIS=BSPLINE
specifies a B-spline basis for the spline expansion. For splines of degree d defined with n knots,
this basis consists of n + d + 1 columns. In order to completely specify the B-spline basis, d leftside boundary knots and maxfd; 1g right-side boundary knots are also required. See the suboptions
KNOTMETHOD=, DATABOUNDARY, KNOTMIN=, and KNOTMAX= for details about how to
specify the positions of both the internal and boundary knots. This is the default if you do not specify
the BASIS= suboption.
404 F Chapter 19: Shared Concepts and Topics
BASIS=TPF(options)
specifies a truncated power function basis for the spline expansion. For splines of degree d defined
with n knots for a variable x, this basis consists of an intercept, polynomials x, x 2 ; : : : ; x d and one
truncated power function for each of the n knots. Unlike the B-spline basis, no boundary knots are
required. See the suboption KNOTMETHOD= for details about how you can specify the position of
the internal knots.
You can modify the number of columns when you request BASIS=TPF with the following options:
NOINT
excludes the intercept column.
NOPOWERS
excludes the intercept and polynomial columns.
DATABOUNDARY
specifies that the extremes of the data be used as boundary knots when building a B-spline basis.
DEGREE=n
specifies the degree of the spline transformation. The degree must be a nonnegative integer. The
degree is typically a small integer, such as 0, 1, 2, or 3. The default is DEGREE=3.
DETAILS
requests tables that show the knot locations and the knots associated with each spline basis function.
KNOTMAX=value
specifies that, for each variable in the EFFECT statement, the right-side boundary knots be equally
spaced starting at the maximum of the variable and ending at the specified value. This option is ignored for variables whose maximum value is greater than the specified value or if the DATABOUNDARY option is also specified.
KNOTMETHOD=knot-method< (knot-options) >
specifies how to construct the knots for spline effects. You can choose from the following knotmethods and affect the knot construction further with the method-specific knot-options:
EQUAL< (n) >
specifies that n equally spaced knots be positioned between the extremes of the data. The default
is n = 3. For a B-spline basis, any needed boundary knots continue to be equally spaced unless
the DATABOUNDARY option has also been specified. KNOTMETHOD=EQUAL is the default
if no knot-method is specified.
LIST(number-list)
specifies the list of internal knots to be used in forming the spline basis columns. For a B-spline
basis, the data extremes are used as boundary knots.
LISTWITHBOUNDARY(number-list)
specifies the list of all knots that are used in forming the spline basis columns. When you use a
truncated power function basis, this list is interpreted as the list of internal knots. When you use
a B-spline basis of degree d, then the first d entries are used as left-side boundary knots and the
last MAX.d; 1/ entries in the list are used as right-side boundary knots.
Spline Effects F 405
MULTISCALE< (multiscale-options) >
specifies that multiple B-spline bases be generated, corresponding to sets with an increasing
number of internal knots. As you increase the number of internal knots, the spline basis you
generate is able to approximate features of the data at finer scales. So, by generating bases at
multiple scales, you facilitate the modeling of both coarse- and fine-grained features of the data.
For scale i, the spline basis corresponds to 2i equally spaced internal knots. By default, the
bases for scales 0–7 are generated. For each scale, a separate spline effect is generated. The
name of the constructed spline effect at scale i is formed by appending _Si to the effect name
that you specify in the EFFECT statement. If you specify multiple variables in the EFFECT
statement, then spline bases are generated separately for each variable at each scale and the name
of the corresponding effect is obtained by appending the variable name followed by _Si to the
name in the EFFECT statement. For example, the following statement generates effects named
spl_x1_S0, spl_x1_S1, spl_x1_S2, : : :, spl_x1_S7 and spl_x2_S1, spl_x2_S2, : : :, spl_x2_S7:
EFFECT spl = spline(x1 x2 / knotmethod=multiscale);
The MULTISCALE option is ignored if you specify the BASIS=TPF spline-option. The MULTISCALE option is not available for spline effects that are specified in the RANDOM statement
of the GLIMMIX procedure.
You can control which scales are included with the following multiscale-options:
STARTSCALE=n
specifies the start scale, where n is a positive integer. The default is STARTSCALE=0.
ENDSCALE=n
specifies the end scale, where n is a positive integer. The default is ENDSCALE=7.
PERCENTILES(n)
requests that internal knots be placed at n equally spaced percentiles of the variable or variables
named in the EFFECT statement. For example, the following statement positions internal knots
at the deciles of the variable x. For a B-spline basis, the extremes of the data are used as boundary
knots:
EFFECT spl = spline(x / knotmethod=percentiles(9));
RANGEFRACTIONS(fraction-list)
requests that internal knots be placed at each fraction of the ranges of the variables in the EFFECT statement. For example, if variable x1 ranges between 1 and 3, and variable x2 ranges
between 0 and 20, then the following EFFECT statement uses internal knots 1.2, 2, and 2.5 for
variable x1 and internal knots 2, 10, and 15 for variable x2:
EFFECT spl = spline(x1 x2 / knotmethod=rangefractions(.1 .5 .75));
For a B-spline basis, the data extremes are used as boundary knots.
406 F Chapter 19: Shared Concepts and Topics
KNOTMIN=value
specifies that for each variable in the EFFECT statement, the left-side boundary knots be equally
spaced starting at the specified value and ending at the minimum of the variable. This option is ignored
for variables whose minimum value is less than the specified value or if the DATABOUNDARY option
is also specified.
NATURALCUBIC
specifies a natural cubic spline basis for the spline expansion. Natural cubic splines, also known
as restricted cubic splines, are cubic splines that are constrained to be linear beyond the extreme
knots. The natural cubic spline basis that is produced by the EFFECT statement is obtained by starting from the unrestricted truncated power function cubic spline basis that is defined with n distinct
knots and imposes the linearity constraints beyond the extreme knots. This basis consists of an intercept, the polynomial x, and n – 2 functions that are all linear beyond the largest knot. The ith
function, i D 1; 2; : : : ; n 2, is zero to the left of the ith knot, which is called the “break knot.”
See the section “Splines and Spline Bases” on page 406 for details of this basis. You can use the
NOINT and NOPOWERS suboptions of the BASIS=TPF option to suppress the intercept and polynomial x when forming the columns of the natural cubic spline basis. When you specify the NATURALCUBIC option, the options BASIS=BSPLINE, DATABOUNDARY, DEGREE=, and KNOTMETHOD=MULTISCALE are not applicable.
SEPARATE
specifies that when multiple variables are specified in the EFFECT statement, the spline basis for
each variable be treated as a separate effect. The names of these separated effects are formed by
appending an underscore followed by the name of the variable to the name that you specify in the
EFFECT statement. For example, the effect names generated with the following statement are spl_x1
and spl_x2:
EFFECT spl = spline(x1 x2 / separate);
In procedures that support variable selection, such as the GLMSELECT procedure, these two effects
can enter or leave the model independently during the selection process. Separated effects are not
supported in the RANDOM statement of the GLIMMIX procedure.
SPLIT
specifies that each individual column in the design matrix that corresponds to the spline effect be
treated as a separate effect that can enter or leave the model independently. Names for these split
effects are generated by appending the variable name and an index for each column to the name that
you specify in the EFFECT statement. For example, the effects generated for the spline effect in the
following statement are spl_x1:1, spl_x1:2, . . . , spl_x1:7 and spl_x2:1, spl_x2:2, . . . , spl_x2:7:
EFFECT spl = spline(x1 x2 / split);
The SPLIT option is not supported in the GLIMMIX procedure.
Splines and Spline Bases
This section provides details about the construction of spline bases with the EFFECT statement. A spline
function is a piecewise polynomial function in which the individual polynomials have the same degree and
Splines and Spline Bases F 407
connect smoothly at join points whose abscissa values, referred to as knots, are prespecified. You can use
spline functions to fit curves to a wide variety of data.
A spline of degree 0 is a step function with steps located at the knots. A spline of degree 1 is a piecewise
linear function where the lines connect at the knots. A spline of degree 2 is a piecewise quadratic curve
whose values and slopes coincide at the knots. A spline of degree 3 is a piecewise cubic curve whose
values, slopes, and curvature coincide at the knots. Visually, a cubic spline is a smooth curve, and it is the
most commonly used spline when a smooth fit is desired. Note that when no knots are used, splines of
degree d are simply polynomials of degree d.
More formally, suppose you specify knots k1 < k2 < k3 < < kn . Then a spline of degree d 0 is a
function S.x/ with d – 1 continuous derivatives such that
8
x < k1
< P0 .x/
Pi .x/
ki x < ki C1 I i D 1; 2; : : : ; n 1
S.x/ D
:
Pn .x/
x kn
where each Pi .x/ is a polynomial of degree d. The requirement that S.x/ has d – 1continuous derivatives is
satisfied by requiring that the function values and all derivatives up to order d – 1 of the adjacent polynomials
at each knot match.
A counting argument yields the number of parameters that define a spline with n knots. There are n + 1
polynomials of degree d, giving .n C 1/.d C 1/ coefficients. However, there are d restrictions at each of the
n knots, so the number of free parameters is .n C 1/.d C 1/ nd = n + d + 1. In mathematical terminology
this says that the dimension of the vector space of splines of degree d on n distinct knots is n + d + 1. If you
have n + d + 1 basis vectors, then you can fit a curve to your data by regressing your dependent variable by
using this basis for the corresponding design matrix columns. In this context, such a spline is known as a
regression spline. The EFFECT statement provides a simple mechanism for obtaining such a basis.
If you remove the restriction that the knots of a spline must be distinct and allow repeated knots, then you
can obtain functions with less smoothness and even discontinuities at the repeated knot location. For a spline
of degree d and a repeated knot with multiplicity m d , the piecewise polynomials that join such a knot
are required to have only d – m matching derivatives. Note that this increases the number of free parameters
by m – 1 but also decreases the number of distinct knots by m – 1. Hence the dimension of the vector space
of splines of degree d with n knots is still n + d + 1, provided that any repeated knot has a multiplicity less
than or equal to d.
The EFFECT statement provides support for the commonly used truncated power function basis and Bspline basis. With exact arithmetic and by using the complete basis, you obtain the same fit with either of
these bases. The following sections provide details about constructing spline bases for the space of splines
of degree d with n knots that satisfies k1 k2 k3 < kn .
Truncated Power Function Basis
A truncated power function for a knot ki is a function defined by
0
x < ki
ti .x/ D
d
.x ki /
x ki
Figure 19.1 shows such functions for d = 1 and d = 3 with a knot at x = 1.
408 F Chapter 19: Shared Concepts and Topics
Figure 19.1 Truncated Power Functions with Knot at x = 1
The name is derived from the fact that these functions are shifted power functions that get truncated to zero
to the left of the knot. These functions are piecewise polynomial functions with two pieces whose function
values and derivatives of all orders up to d 1 are zero at the defining knot. Hence these functions are
splines of degree d. It is easy to see that these n functions are linearly independent. However, they do not
form a basis, because such a basis requires n C d C 1 functions. The usual way to add d C 1 additional basis
functions is to use the polynomials 1; x; x 2 ; : : : ; x d . These d C 1 functions together with the n truncated
power functions ti .x/; i D 1; 2; : : : ; n form the truncated power basis.
Note that each time a knot is repeated, the associated exponent used in the corresponding basis function
is reduced by 1. For example, for splines of degree d with three repeated knots ki D ki C1 D ki C2 the
corresponding basis functions are ti .x/ D .x ki /dC , ti C1 .x/ D .x ki /dC 1 , and ti C2 .x/ D .x ki /dC 2 .
Provided that the multiplicity of each repeated knot is less than or equal to the degree, this construction
continues to yield a basis for the associated space of splines.
The main advantage of the truncated power function basis is the simplicity of its construction and the ease
of interpreting the parameters in a model that corresponds to these basis functions. However, there are
two weaknesses when you use this basis for regression. These functions grow rapidly without bound as x
increases, resulting in numerical precision problems when the x data span a wide range. Furthermore, many
or even all of these basis functions can be nonzero when evaluated at some x value, resulting in a design
matrix with few zeros that precludes the use of sparse matrix technology to speed up computation. This
weakness can be addressed by using a B-spline basis.
B-Spline Basis
A B-spline basis can be built by starting with a set of Haar basis functions, which are functions that are 1
between adjacent knots and 0 elsewhere, and then applying a simple linear recursion relationship d times,
yielding the n C d C 1 needed basis functions. For the purpose of building the B-spline basis, the n
prespecified knots are referred to as internal knots. This construction requires d additional knots, known
as boundary knots, to be positioned to the left of the internal knots, and MAX.d; 1/ boundary knots to be
positioned to the right of the internal knots. The actual values of these boundary knots can be arbitrary. The
EFFECT statement provides several methods for placing the needed boundary knots, including the common
method of using repeated values of the data extremes as the boundary knots. The boundary knot placement
Splines and Spline Bases F 409
affects the precise form of the basis functions that are generated, but it does not affect the following two
desirable properties:
1. The B-spline basis functions are nonzero over an interval that spans at most d C 2 knots. This yields
design matrix columns each of whose rows contain at most d C 2 adjacent nonzero entries.
2. The computation of the basis functions at any x value is numerically stable and does not require
evaluating powers of this value.
The following figures show the B-spline bases defined on Œ0; 1 with four equally spaced internal knots at
0.2, 0.4, 0.6, and 0.8.
Figure 19.2 shows a linear B-spline basis. Note that this basis consists of six functions each of which is
nonzero over an interval that spans at most three knots.
Figure 19.2 Linear B-Spline Basis with Four Equally Spaced Interior Knots
Figure 19.3 shows a cubic B-spline basis where the needed boundary knots are positioned at x = 0 and x = 1.
Note that this basis consists of eight functions, each of which is nonzero over an interval spanning at most
five knots.
410 F Chapter 19: Shared Concepts and Topics
Figure 19.3 Cubic B-Spline Basis with Four Equally Spaced Interior Knots
Figure 19.4 shows a different cubic B-spline basis where the needed left-side boundary knots are positioned
at –0.6, –0.4, –0.2, and 0. The right-side boundary knots are positioned at 1, 1.2, 1.4, and 1.6. Note that, as
in the basis shown in Figure 19.3, this basis consists of eight functions, each of which is nonzero over an
interval spanning at most five knots. The different positioning of the boundary knots has merely changed
the shape of the individual basis functions.
Figure 19.4 Cubic B-Spline Basis with Equally Spaced Boundary and Interior Knots
You can find details about this construction in Hastie, Tibshirani, and Friedman (2001).
EFFECTPLOT Statement F 411
Natural Cubic Spline Basis
Natural cubic splines are cubic splines with the additional restriction that the splines are required to be
linear beyond the extreme knots. Some authors use the terminology “restricted cubic splines” in preference
to the terminology “natural cubic splines.” The space of unrestricted cubic splines on n knots has dimension
n C 4. Imposing the restrictions that the cubic polynomials beyond the first and last knot reduce to linear
polynomials reduces the number of degrees of freedom by 4, and so a basis for the natural cubic splines
consists of n functions. Starting from the truncated power function basis for the unrestricted cubic splines,
you can obtain a reduced basis by imposing linearity constraints. You can find details about this construction
in Hastie, Tibshirani, and Friedman (2001). Figure 19.5 shows this natural cubic spline basis defined on
Œ0; 1 with four equally spaced internal knots at 0.2, 0.4, 0.6, and 0.8. Note that this basis consists of four
basis functions that are all linear beyond the extreme knots at 0.2 and 0.8.
Figure 19.5 Natural Cubic Spline Basis with Four Equally Spaced Knots
EFFECTPLOT Statement
This statement applies to the following procedures:
GENMOD, LOGISTIC, ORTHOREG, and PLM.
The EFFECTPLOT statement produces a display (effect plot) of a complex fitted model and provides options
for changing and enhancing the displays. One simple effect plot is the display for a linear regression of the
response Y on a single predictor X: the regression line is drawn with the predicted response on the Y axis
and the covariate on the X axis. The regression line can be enhanced by displaying the observations and
adding confidence and prediction limits. When your model is more complicated—with more continuous and
categorical covariates, nestings and interactions, and link functions—the effect plots display the behavior of
some covariates over their ranges while fixing other covariates at some fixed values; this can enable easier
interpretation and explanation of the resulting model.
By default, a single plot is produced based on the type of response variable and the number of continuous
and classification covariates in the model. You can also specify options to do the following:
412 F Chapter 19: Shared Concepts and Topics
select the variables to display on the plots
produce multiple plots based on the following: the levels of classification covariates; the minimum,
maximum, mean or middle (midrange) value of continuous covariates; and specified values of the
covariates
specify different fixed values for continuous and classification covariates that are not displayed on the
plot
panel and unpanel plots
select variables to slice or group by
display (or remove from display) observations and confidence limits
Syntax: EFFECTPLOT Statement
EFFECTPLOT < plot-type < (plot-definition-options) > > < / options > ;
The available plot-types and their plot-definition-options are described in Table 19.13. Table 19.15 lists
the options that can be specified after a slash (/) for any plot-type, and Table 19.16 lists additional options
that enhance specific plot-types. Full descriptions of the plot-definition-options and the other options are
provided in the section “Dictionary of Options” on page 414.
Table 19.13 Plot-Types and Plot-Definition-Options
Plot-Type and Description
Plot-Definition-Options
BOX
Displays a box plot of continuous response data at
each level of a CLASS effect, with predicted values
superimposed and connected by a line. This is an
alternative to the INTERACTION plot-type.
PLOTBY= variable or CLASS effect
X= CLASS variable or effect
CONTOUR
Displays a contour plot of predicted values against
two continuous covariates.
PLOTBY= variable or CLASS effect
X= continuous variable
Y= continuous variable
FIT
Displays a curve of predicted values versus a
continuous variable.
PLOTBY= variable or CLASS effect
X= continuous variable
INTERACTION
Displays a plot of predicted values (possibly with
error bars) versus the levels of a CLASS effect. The
predicted values are connected with lines and can be
grouped by the levels of another CLASS effect.
PLOTBY= variable or CLASS effect
SLICEBY= variable or CLASS effect
X= CLASS variable or effect
Syntax: EFFECTPLOT Statement F 413
Table 19.13 continued
Plot-Type and Description
Plot-Definition-Options
SLICEFIT
Displays a curve of predicted values versus a
continuous variable grouped by the levels of a
CLASS effect.
PLOTBY= variable or CLASS effect
SLICEBY= variable or CLASS effect
X= continuous variable
By default, a single plot is produced based on the type of response variable and the number of continuous and
classification covariates in the model as shown in Table 19.14. If you have a polytomous response model,
then the response variable is treated as the grouping classification variable in this table. If your model does
not fit into Table 19.14, then a default plot is not produced; however, specifying the plot-type argument
displays a plot with the extra continuous covariates fixed at their mean values and the extra classification
covariates fixed at their reference levels.
Table 19.14 Default Plot-Types
Number of Covariates
Classification Continuous
1
2
0
0
1
0
0
1
2
1
Type of Response Variable
Continuous or Binary
Polytomous
INTERACTION
INTERACTION with groups
FIT
CONTOUR
SLICEFIT
INTERACTION with groups
None
SLICEFIT
None
None
Table 19.15 and Table 19.16 list the options that can be specified after a slash (/) to enhance the effect plots.
Table 19.15
Available Options for All Plot-Types
AT< args >
ATLEN=
ATORDER=
LINK
MOFF
NCOLS=
OBS< (options) > PLOTBYLEN= PREDLABEL=
Not available for the BOX plot-type
ILINK
NOOBS
UNPACK
INDIVIDUAL
NROWS=
N OTE : If your model contains an offset variable and the MOFF option is not specified or not valid, then
the predicted values are computed only at the observations. In this case, the FIT and SLICEFIT plottypes display scatter plots of the predicted values, the CONTOUR plot-type displays the residuals against
two continuous covariates but with no fitted surface, the INTERACTION plot-type does not connect the
predicted values with lines, and the BOX plot-type is unchanged.
414 F Chapter 19: Shared Concepts and Topics
Table 19.16
Additional Options for Each Plot-Type
Plot-Type
Options
BOX
CLUSTER
YRANGE=
CONNECT
CONTOUR
EXTEND=
GRIDSIZE=
FIT
ALPHA=
NOCLM
INTERACTION
SLICEFIT
NOCLUSTER
NOCONNECT
EXTEND=
NOLIMITS
GRIDSIZE=
SMOOTH
NOCLI
YRANGE=
ALPHA=
CONNECT
POLYBAR
CLI
LIMITS
YRANGE=
CLM
NOCLUSTER
CLUSTER
NOCONNECT
ALPHA=
GRIDSIZE=
CLI
LIMITS
CLM
YRANGE=
EXTEND=
Dictionary of Options
This section describes the EFFECTPLOT options in alphabetical order.
ALPHA=value
specifies the significance level, 0 value 1, for producing 100.1
fidence limits. By default, value=0.05.
value=2/% prediction and con-
AT < contopt > < classopt > < variable1=varopt < variable2=varopt. . . > >
where contopt= MEAN | MIN | MAX | MIDRANGE
classopt= ALL | REF
varopt= contopts | number-list | classopts | ’class-level’. . . ’class-level’
specifies values at which to fix continuous and class variables when they are not used in X=, Y=,
SLICEBY=, or PLOTBY= effects. The contopt keyword fixes continuous variables at their mean,
minimum, maximum, or midrangeD 21 .minimum C maximum/; the default is to use the mean. The
classopt keyword either fixes a CLASS variable at its reference (last) level or indicates that all levels
of the CLASS variable should be processed; the default is to use the reference level. The varopt
values enable you to specify contopt and classopt keywords, or to specify lists of numbers or class
levels. You can specify a CLASS variable only once in the AT specification, but you can specify a
continuous variable multiple times; for example, the following syntax is valid when X is a continuous
variable:
effectplot / at(x=min max x=0 to 2 by 1 x=2 5 7);
Duplicate AT values are suppressed, so the last X=2 value is ignored.
You can also specify plug-in values for CLASS variable levels when computing the predicted values
x0 ˇ. For example, suppose a CLASS variable A with two levels={0,1} is in the model. Then instead of
using the coding for A in the x vector by specifying AT(A=all), AT(A=ref) or AT(A=’0’ ’1’), you
can specify a numeric list to plug in. For example, if the proportion of A’s that equal 0 in the data set
is 0.3, then you can input the proportions for all levels of the variable by specifying AT(A=0.3 0.7).
Under GLM coding, A=0 is coded as “1 0” and A=1 is coded as “0 1”, so the plug-in specification
Syntax: EFFECTPLOT Statement F 415
replaces both of these codings with “0.3 0.7”. Under REFERENCE coding A=0 is coded as “1” and
A=1 is coded as “0”, so this specification replaces both of these codings with “0.3” followed by “0.7”;
however, if another variable is nested within A, then only “0.3” is used. To plug in values, you must
specify a multiple of the number of parameters used for the CLASS variable or, if a variable is nested
within the CLASS variable, a multiple of the number of levels of the CLASS variable.
The plug-in values are distributed through the rest of the model effects in the following fashion. If
a variable is nested within a plug-in variable, then its coding is multiplied by the plug-in value for
the level it is nested in. If a variable interacts with a plug-in variable, its coding is multiplied by
the appropriate plug-in value for the level it is interacting with. Lag, multimember, polynomial, and
spline constructed effects are affected only by interactions and nestings. If the plug-in variable is part
of a collection effect, then its values are replaced by the plug-in values; collection effects are also
affected by interactions and nestings.
The AT levels are used for computing the predicted values. If the OBS option is also specified, then all
observations are still displayed on all of the plots. For example, if you specify the options AT(A=’1’)
OBS, then the fitted values are computed with A=1, but all of the observations are displayed with their
predicted values computed at their observed level of A. If you want to display only a subset of the
observations based on the levels of a CLASS variable, then you must specify either the PLOTBY=
option or the OBS(BYAT) option.
ATLEN=n
specifies the maximum length (1n256) of the levels of the AT variables that are displayed in
footnotes and headers. By default, up to 256 characters of the CLASS levels are displayed, and the
continuous AT levels are displayed with a BEST format that has a width greater than or equal to 5,
which distinguishes each level. C AUTION : If the levels of your AT variables are not unique when
the first n characters are displayed, then the levels are combined in the plots but not in the underlying
computations. Also, at most n characters for continuous AT variables are displayed.
ATORDER=ASCENDING | DESCENDING
uses the AT values for continuous variables in ascending or descending order as specified. By default,
values are used in the order of their first appearance in the AT option.
CLI
displays normal (Wald) prediction limits. This option is available only for normal distributions with
identity links. If your model is from a Bayesian analysis, then sampling-based intervals are computed;
see the section “Analysis Based on Posterior Estimates” on page 5833 in Chapter 69, “The PLM
Procedure,” for more information.
CLM
displays confidence limits. These are computed as the normal (Wald) confidence limits for the linear
predictor, and if the ILINK option is specified, the limits are also back-transformed by the inverse link
function. If your model is from a Bayesian analysis, then sampling-based intervals are computed;
see the section “Analysis Based on Posterior Estimates” on page 5833 in Chapter 69, “The PLM
Procedure,” for more information.
CLUSTER< =percent >
modifies the BOX and INTERACTION plot-types by displaying the levels of the SLICEBY= effect
in a side-by-side fashion. You can specify percent as a percentage of half the distance between X
levels. The percent value must be between 0.1 and 1; the default percent depends on the number
416 F Chapter 19: Shared Concepts and Topics
of X levels, the number of SLICEBY levels, and the number of PLOTBY levels for INTERACTION
plot-types. Default clustering can be removed by specifying the NOCLUSTER option.
CONNECT
modifies the BOX and INTERACTION plot-types by connecting the predicted values with a line.
Default connecting lines can be removed by specifying the NOCONNECT option.
EXTEND=DATA | value
extends continuous covariate axes by value 12 range in both directions, where range is the range
of the X axis. Specifying the DATA keyword displays curves to the range of the data within the
appropriate SLICEBY=, PLOTBY=, and AT level. For the CONTOUR plot-type, value=0.05 by
default; other plot-types set the default value to 0. When constructed effects are present, only the
EXTEND=DATA option is available.
GRIDSIZE=n
specifies the resolution of curves by computing the predicted values at n equally spaced x-values
and specifies the resolution of surfaces by computing the predicted values on an nn grid of points.
Default values are n = 200 for curves and bands, n = 50 for surfaces, and n = 2 for lines. If results of
a Bayesian or bootstrap analysis are being displayed, then the defaults are n = 500000/B, where B is
the number of samples, the upper limit is equal to the usual defaults, and the lower limit equal to 20.
ILINK
displays the fit on the scale of the inverse link function. In particular, the results are displayed on the
probability scale for logistic regression. By default, a procedure displays the fit on either the link or
inverse link scale.
INDIVIDUAL
displays individual probabilities for polytomous response models with cumulative links on the scale
of the inverse link function. This option is not available when the LINK option is specified, and
confidence limits are not available with this option.
LIMITS
invokes the CLI and CLM options.
LINK
displays the fit on the scale of the link function; that is, the linear predictor. Note that probabilities or
observed proportions near 0 and 1 are transformed to ˙20. By default, a procedure displays the fit on
either the link or inverse link scale.
MOFF
moves the offset for a Poisson regression model to the response side of the equation. If the ILINK
option is also in effect, then the rate is displayed on the Y axis, while the LINK option displays the
log of the rate on the Y axis. Without this option, the predicted values are computed and displayed
only for the observations.
NCOLS=n
specifies the maximum number of columns in a paneled plot. This option is not available with the
BOX plot-type.
The default choice of NROWS= and NCOLS= is based on the number of PLOTBY= and AT levels.
If there is only one plot being displayed in a panel, then NROWS=1 and NCOLS=1 and the plots are
Syntax: EFFECTPLOT Statement F 417
produced as if you specified only the UNPACK option. If only two plots are displayed in a panel,
then NROWS=1 and NCOLS=2. For all other cases, a 2x2, 2x3, or 3x3 panel is chosen based on how
much of the last panel is used, with ties going to the larger panels. For example, if 14 plots are being
created, then this requires either four 2x2 panels with 50% of the last panel filled, three 2x3 panels
with 33% of the last panel filled, or two 3x3 panels with 55% of the last panel filled; in this case, the
3x3 panels are chosen.
If you specify both of the NROWS= and NCOLS= options, then those are the values used. However, if
you only specify one of the options but have fewer plots, then the panel size is reduced; for example,
if you specify NROWS=6 but only have four plots, then a plot with four rows and one column is
produced.
NOCLI
suppresses the prediction limits.
NOCLM
suppresses the confidence limits.
NOCLUSTER
modifies the BOX and INTERACTION plot-types by preventing the side-by-side display of the levels
of the SLICEBY= effect.
NOCONNECT
modifies the BOX and INTERACTION plot-types by suppressing the line that connects the predicted
values.
NOLIMITS
invokes the NOCLI and NOCLM options.
NOOBS
suppresses the display of observations and overrides the specification of the OBS= option.
NROWS=n
specifies the maximum number of rows in a paneled plot. This option is not available with the BOX
plot-type. See the NCOLS= option for more details.
OBS< (obs-options) >
displays observations on the effect plots. An input data set is required; hence the OBS option is
not available with PROC PLM. The OBS option is overridden by the NOOBS option. When the
ILINK option is specified with binary response variables, then either the observed proportions or a
coded value of the response is displayed. For polytomous response variables, the observed values are
overlaid onto the fitted curves unless the LOCATION= option is specified. Whether observations are
displayed by default or not depends upon the procedure. If the PLOTBY= option is specified, then
the observations displayed on each plot are from the corresponding PLOTBY= level for classification
effects; for continuous effects, all observations are displayed on every plot.
The following obs-options are available:
BYAT
subsets the observations by AT level and by the PLOTBY= level. If you specify the PLOTBY=
option without specifying this option, the observations are displayed on the plots that correspond
to their PLOTBY= level without regard to any classification variables specified in the AT option.
418 F Chapter 19: Shared Concepts and Topics
However, for FIT plot-types a distance can be computed and displayed (see the DISTANCE
option for more information). This option is ignored when there are no AT variables.
CDISPLAY=NONE | OUTLINE | GRADIENT | OUTLINEGRADIENT
controls the display of observations on contour plots. The keyword OUTLINE displays the observations as circles, GRADIENT displays gradient-colored dots, OUTLINEGRADIENT displays gradient-filled-circles, and NONE suppresses the display of the observations. The default
is CDISPLAY=OUTLINEGRADIENT.
CGRADIENT=RESIDUAL | DEPENDENT
specifies what the gradient-shading of the observed values on the CONTOUR plot-type represents. The RESIDUAL keyword shades the observations by the raw residual value and displays
the fitted surface as a line contour plot. The DEPENDENT keyword shades the observations by
the response variable value and displays the fitted surface as a contour shaded on the same scale.
The default is CGRADIENT=DEPENDENT.
DEPTH=depth
specifies the number of overlapping observations that can be distinguished by adjusting their
transparency; you can specify 1 depth 100. By default, DEPTH=1. The DEPTH= option
is available with FIT, SLICEFIT, and INTERACTION plot-types.
DISTANCE
displays observations on FIT plot-types with a color-gradient that indicates how far the observation is from the AT and PLOTBY= level. This option is ignored unless an AT or PLOTBY=
option is specified.
The distance is computed as the square root of the following number: for each continuous AT
and PLOTBY= variable, add the square of the difference from the observed value divided by
the range of the variable; for each CLASS AT and PLOTBY= variable, add 1 if the CLASS
levels are different. Thus the largest possible distance is the square root of the number of AT
and PLOTBY= variables. Observations at zero distance are displayed with the darkest color,
and the color fades as the distance increases.
Note that the UNPACKed panels compute the maximum distance within each panel and hence
do not use the same gradient across all panels. Also, the PANELS panel-type computes the maximum distance within each PLOTBY= level, so a different gradient is used for each PLOTBY=
level. All other panel-types compute the maximum distance across all observations and therefore use the same gradient on every plot.
FITATCLASS
computes fitted values only for class levels that are observed in the data set. This option is
ignored when the GLM parameterization is used.
FRINGE
displays observations in a fringe (rug) plot at the bottom of the plot. This option is available
only with FIT and SLICEFIT plot-types.
JITTER< (jitter-options) >
shifts (jitters) the observations. By default, the jittering in the X direction is achieved by adding
a random number that is generated according to a normal distribution with mean=0 and standard
deviationD jitter=2 and truncating at ˙jitter, where jitter=0.01 times the range of the X axis;
Syntax: EFFECTPLOT Statement F 419
the jittering in the Y direction is performed independently but in the same fashion. The JITTER
option is not available with the BOX plot-type. The following jitter-options are available:
FACTOR=factor sets the jitter to factor times the range of the axis, and jitters in both the X
and Y directions. You can specify 0 factor 1.
SEED=seed specifies an integer to use as the initial seed for the random number generator. If
you do not specify a seed, or if you specify a value less than or equal to zero, then the
time of day from the computer clock is used to generate an initial seed.
X=x-jitter
sets the jitter to x-jitter for the X direction; the jitter in the Y direction is assumed
to be 0 unless the Y= option is also specified. You can specify x-jitter 0. The X=
option is not available for the INTERACTION plot-type. This option is ignored if the
FACTOR= option is also specified.
Y=y-jitter
sets the jitter to y-jitter for the Y direction; the jitter in the X direction is assumed to
be 0 unless the X= option is also specified. You can specify y-jitter 0. This option
is ignored if the FACTOR= option is also specified.
LABEL< =OBS >
labels markers with their observation number.
LOCATION=location
specifies where the observed values for polytomous response models are displayed when the
SLICEBY= variable is the response. This option is available only with the SLICEFIT and
INTERACTION plot-types. The observations are always displayed at their appropriate X-axis
value, but their Y-axis location can depend on the specification of the YRANGE= option or on
the minimum and maximum computed predicted values in addition to the specified location.
The following locations are available:
BOTTOM< =factor > displays the first response level at the minimum predicted value, and
displays succeeding response levels above the first level at factor range intervals,
where range is the range of the predicted values. You can specify 0 factor 1, but
the largest usable value, which corresponds to LOCATION=SPREAD, is factor D
1
, where k C 1 is the number of response levels that are displayed. By default,
k
factor D 0:03.
CURVE
displays the observations for polytomous response models at their predicted values.
For displays on the LINK scale, the reference level is displayed at the maximum
value. This method is the default.
FIRST
displays the observations for a response level at the first displayed predicted value for
that response level.
MAX
displays the observations for a response level at the maximum displayed predicted
value for that response level.
MIDDLE
displays the observations for a response level at the middle of the displayed predicted values for that response level.
MIN
displays the observations for a response level at the minimum displayed predicted
value for that response level.
SPREAD
displays the observations with the response levels evenly spread across the Y axis.
420 F Chapter 19: Shared Concepts and Topics
TOP< =factor > displays the last response level at the maximum predicted value, and displays
preceding response levels below the last level at factor range intervals, where range
is the range of the predicted values. You can specify 0 factor 1, but the largest
usable value, which corresponds to LOCATION=SPREAD, is factor D k1 , where
k+1 is the number of response levels that are displayed. By default, factor D 0:03.
PLOTBY< (panel-type) >=effect< =numeric-list >
specifies a variable or CLASS effect at whose levels the predicted values are computed and the plots
are displayed. You can specify the response variable as the effect for polytomous response models.
The panel-type argument specifies the method in which the plots are grouped for the display. The
following panel-types are available.
COLUMNS
specifies that the columns within each panel correspond to different levels of the PLOTBY=
effect and hence the rows correspond to different AT levels.
PACK
specifies that plots be displayed in the panels as they are produced with no control over the
placement of the PLOTBY= and AT levels.
PANELS | LEVELS
specifies that each level of the PLOTBY= effect begin a new panel of plots and the AT levels
define the plots within the panels.
ROWS
specifies that the rows within each panel correspond to different levels of the PLOTBY= effect
and hence the columns correspond to different AT levels.
This option is ignored with the BOX plot-type; box plots are always displayed in an unpacked fashion,
grouped by the PLOTBY= and AT levels. If you specify a continuous variable as the effect, then you
can either specify a numeric-list of values at which to display that variable or, by default, five equally
spaced values from the minimum variable value to its maximum are displayed.
The default panel-type is based on the number of PLOTBY= and AT levels as shown in the following
table.
Number of
PLOTBY Levels
1
>1
1
2
3
>3
Number of
AT Levels
1
1
>1
>1
>1
>1
Resulting
panel-type
(UNPACK)
PACK
PACK
ROWS
COLUMNS
PANELS
The default dimensions of the panels are also based on the number of PLOTBY= and AT levels; see
the NCOLS= option for details.
Specification of the panel-type is honored except in the following cases. If you specify a panel-type
but produce only one plot, specify the NROWS=1 and NCOLS=1 options, or specify the UNPACK
Syntax: EFFECTPLOT Statement F 421
option, then the plots are produced as if you specified only the UNPACK option. If you specify the
PANELS panel-type with only one AT level, then the plots are produced with the UNPACK option.
However, if you specify the PANELS panel-type but the PLOTBY= effect has only one level, then
the panel-type is changed to PACK.
PLOTBYLEN=n
specifies the maximum length (1 n 256) of the levels of the PLOTBY= variables, which are displayed in footnotes and headers. By default, up to 256 characters of the CLASS levels are displayed.
C AUTION : If the levels of your PLOTBY= variables are not unique when the first n characters are
displayed, then the levels are combined in the plots but not in the underlying computations.
POLYBAR
displays polytomous response data as a stacked histogram with bar heights defined by the individual
predicted value. Your response variable must be the effect specified in the SLICEBY= option. If you
specify the INDIVIDUAL option, then the histogram bars are displayed in a side-by-side fashion. If
you specify the CLM option, then error bars are displayed on the side-by-side histogram bars.
PREDLABEL=‘label’
specifies a label to be displayed on the Y axis. The default Y axis label is determined by your model.
For the CONTOUR plot-type, this option changes the title to “label for Y.”
SHOWCLEGEND
displays the gradient-legend for the CONTOUR plot-type. This option has no effect when the
OBS(CGRADIENT=RESIDUAL) option is also specified.
SLICEBY=NONE | effect< =numeric-list >
displays the fitted values at the different levels of the specified variable or CLASS effect. You can
specify the response variable as the effect for polytomous response models. Use this option to modify
SLICEFIT, INTERACTION, and BOX plot-types. If you specify a continuous variable as the effect,
then you can either specify a numeric-list of values at which to display that variable or, by default,
five equally spaced values from the minimum variable value to its maximum are displayed. The
NONE keyword is available for preventing the INTERACTION plot-type from slicing by a second
class covariate. Note that the SLICEBY=NONE option is not available for the SLICEFIT plot-type,
since that is the same as the FIT plot-type. The BOX plot-type accepts only classification effects.
SMOOTH
overlays a loess smooth on the FIT plot-type for models that have only one continuous predictor. This
option is not available for binary or polytomous response models.
UNPACK
suppresses paneling. By default, multiple plots can appear in some output panels. Specify UNPACK
to display each plot separately.
X=effect
specifies values to display on the X axis. For BOX and INTERACTION plot-types, effect can be a
CLASS effect in the MODEL statement. For FIT, SLICEFIT, and CONTOUR plot-types, effect can
be any continuous variable in the model.
422 F Chapter 19: Shared Concepts and Topics
Y=args
specifies values to display on the Y axis for the CONTOUR plot-type. The Y= argument can be any
continuous variable in the model.
YRANGE=CLIP | (< min >< ,max >)
displays the predicted values on the Y axis in the range [min,max ]. The YRANGE=CLIP option has
the same effect as specifying the minimum predicted value as min and the maximum predicted value
as max. The axis might extend beyond your specified values. By default, when the Y axis displays
predicted probabilities, the entire Y axis, [0,1], is displayed. This option is useful if your predicted
probabilities are all contained in some subset of this range. This option is not available with the
CONTOUR plot-type.
ODS Graphics: EFFECTPLOT Statement
To produce the EFFECTPLOT displays, ODS Graphics must be enabled. For more information about ODS
Graphics, see Chapter 21, “Statistical Graphics Using ODS.” The available graph names are provided in
Table 19.17.
Table 19.17 Graphs Produced by the EFFECTPLOT Statement
ODS Graph Name
Plot Description
BoxFitPlot
A box plot of the responses at each level of one classification effect, overlaid with a plot of the predicted values
A contour plot of the fitted surface against two continuous covariates
A panel of ContourFitPlots
A curve of the predicted values plotted against one continuous covariate
A panel of FitPlots
A plot of the predicted values (connected by a line) against one classification effect, possibly for each level of a second classification effect
A panel of InteractionPlots
A curve of the predicted values against one continuous covariate for each
level of a second classification covariate
A panel of SliceFitPlots
ContourFitPlot
ContourFitPanel
FitPlot
FitPanel
InteractionPlot
InteractionPanel
SliceFitPlot
SliceFitPanel
Examples: EFFECTPLOT Statement F 423
Examples: EFFECTPLOT Statement
Example 19.1: A Saddle Surface
Myers (1976) analyzes an experiment reported by Frankel (1961) which is aimed at maximizing the yield of
mercaptobenzothiazole (MBT) by varying processing time and temperature. Myers uses a two-factor model
in which the estimated surface does not have a unique optimum. The objective is to find the settings of time
and temperature in the processing of a chemical that maximize the yield. The following statements create
the data set d:
data d;
input Time Temp MBT @@;
label Time = "Reaction Time (Hours)"
Temp = "Temperature (Degrees Centigrade)"
MBT = "Percent Yield Mercaptobenzothiazole";
datalines;
4.0 250 83.8
20.0 250 81.7
12.0 250 82.4
12.0 250 82.9
12.0 220 84.7
12.0 280 57.9
12.0 250 81.2
6.3 229 81.3
6.3 271 83.1
17.7 229 85.3
17.7 271 72.7
4.0 250 82.0
;
In the following statements, the ORTHOREG procedure fits a response surface regression model to the
data and uses the EFFECTPLOT statement to create a slice of the response surface. The FIT plot-type
requests plots of the predicted yield against the Time variable, and the PLOTBY= option specifies that the
Temp variable is fixed at five equally spaced values so that five fitted regression curves are displayed in
Output 19.1.1.
ods graphics on;
proc orthoreg data=d;
model MBT=Time|Time|Temp|[email protected];
effectplot fit(x=time plotby=temp);
run;
ods graphics off;
The displays in Output 19.1.1 show that the slope of the surface changes as the temperature increases.
424 F Chapter 19: Shared Concepts and Topics
Output 19.1.1 Panel of Fit Plots
It might be more informative to see these results in one graphic, so the following statements specify the
SLICEFIT plot-type to overlay plots of the predicted yield versus time, fixed at several values of temperature.
In this case, the SLICEBY= option is specified to explicitly use the same four temperatures as used in the
experiment.
ods graphics on;
proc orthoreg data=d;
model MBT=Time|Time|Temp|[email protected];
effectplot slicefit(x=time sliceby=temp=229 250 271 280);
run;
ods graphics off;
Output 19.1.2 shows that you should choose either low temperatures and long times to optimize the yield,
or maybe high temperatures and short times.
Example 19.1: A Saddle Surface F 425
Output 19.1.2 Fit Plot Grouped (Sliced) by Temp
Another plot might explain the reason for this more clearly. The following statements produces the default
EFFECTPLOT statement display, enhanced by the OBS(JITTER) option to jitter the observations so that
you can see the replicated points.
ods graphics on;
proc orthoreg data=d;
model MBT=Time|Time|Temp|[email protected];
effectplot / obs(jitter(seed=39393));
run;
ods graphics off;
426 F Chapter 19: Shared Concepts and Topics
Output 19.1.3 shows the reason for the changing slopes is that the surface is at a saddle point. This surface
does not have an optimum point.
Output 19.1.3 Contour Fit Plot with Jittered Observations
Example 19.2: Unbalanced Two-Way ANOVA
This example uses data from Kutner (1974, p. 98) to illustrate a two-way analysis of variance. The original
data source is Afifi and Azen (1972, p. 166). The following statements create the data set a:
Example 19.2: Unbalanced Two-Way ANOVA F 427
data a;
input drug disease @;
do i=1 to 6;
input y @;
output;
end;
datalines;
1 1 42 44 36 13 19 22
1 2 33 . 26 . 33 21
1 3 31 -3 . 25 25 24
2 1 28 . 23 34 42 13
2 2 . 34 33 31 . 36
2 3 3 26 28 32 4 16
3 1 . . 1 29 . 19
3 2 . 11 9 7 1 -6
3 3 21 1 . 9 3 .
4 1 24 . 9 22 -2 15
4 2 27 12 12 -5 16 15
4 3 22 7 25 5 12 .
;
In the following statements, PROC GENMOD fits two classification variables and their interaction to Y. The
first EFFECTPLOT statement displays the default graphic, which plots the predicted values against Disease
for each of the three Drug levels. The OBS option also displays the observations on the plot. The second
EFFECTPLOT statement modifies the default to plot the predicted values against Drug for each of the three
Disease levels. The CLM option is specified to produce 95% confidence bars for the means.
ods graphics on;
proc genmod data=a;
class drug disease;
model y=disease drug disease*drug / d=n;
effectplot / obs;
effectplot interaction(sliceby=disease) / clm;
run;
ods graphics off;
In Output 19.2.1, the default interaction plot is produced, and the observations are also displayed. From this
plot, you can compare the performance of the drugs for a given disease . The predicted values are connected
with a line to provide something for your eye to follow—obviously a line has no intrinsic meaning in this
graphic. Drugs 3 and 4 are consistently outperformed by the first two drugs.
428 F Chapter 19: Shared Concepts and Topics
Output 19.2.1 Interaction Plot: Default with Observations
By default, the first classification variable is displayed on the X axis and the second classification variable
is used for grouping. Specifying the SLICEBY=DISEASE option in the second EFFECTPLOT statement
reverses this, displays the classification variable with the most levels on the X axis, and slices by fewer
levels, resulting in a more readable display. Output 19.2.2 shows how well a given drug performs on each
disease.
Example 19.2: Unbalanced Two-Way ANOVA F 429
Output 19.2.2 Interaction Plot with Specified SLICEBY= Effect
In the following statements, the BOX plot-type is requested to display box plots of the predictions by each
drug and disease combination. The second EFFECTPLOT statement displays the same information by using
an INTERACTION plot-type and specifies the OBS option to display the individual observations. The third
EFFECTPLOT statement creates an interaction plot of predictions versus drug for each of the Disease
levels, and displays them in a panel.
ods graphics on;
proc genmod data=a;
class drug disease;
model y=drug disease drug*disease / d=n;
effectplot box;
effectplot interaction(x=drug*disease) / obs;
effectplot interaction(plotby=disease);
run;
ods graphics off;
430 F Chapter 19: Shared Concepts and Topics
In the box plot in Output 19.2.3, the predicted values are displayed as circles; they coincide with the mean
of the data at each level which are displayed as diamonds. The predicted values are again connected by
lines. It is difficult to make any conclusions from this graphic.
Output 19.2.3 Box Fit Plot
Example 19.2: Unbalanced Two-Way ANOVA F 431
Output 19.2.4 shows the interaction plot at every combination of Drug and Disease. This plot is identical to
the preceding box plot, except the boxes are replaced by the actual observations. Again, it is difficult to see
any pattern in the plot.
Output 19.2.4 Interaction Plot with Specified X= Effect
432 F Chapter 19: Shared Concepts and Topics
Output 19.2.5 groups the observations by Disease, and for each disease displays the effectiveness of the
four drugs in a panel of plots.
Output 19.2.5 Interaction Plot with Specified PLOTBY= Effect
Example 19.3: Logistic Regression F 433
Example 19.3: Logistic Regression
Consider a study of the analgesic effects of treatments on elderly patients with neuralgia. Two test treatments
and a placebo are compared. The response variable is whether the patient reported pain or not. Researchers
recorded the age and gender of 60 patients and the duration of complaint before the treatment began. The
following DATA step creates the data set Neuralgia:
data Neuralgia;
input Treatment
datalines;
P F 68
1 No
P M 66 26 Yes
A F 71 12 No
A M 71 17 Yes
B F 66 12 No
A F 64 17 No
P M 70
1 Yes
A F 64 30 No
B F 78
1 No
B M 75 30 Yes
A M 70 12 No
B M 70
1 No
P M 78 12 Yes
P M 66
4 Yes
A M 78 15 Yes
P F 72 27 No
B F 65
7 No
P M 67 17 Yes
P F 67
1 Yes
A F 74
1 No
;
$ Sex $ Age Duration Pain $ @@;
B
B
B
A
A
P
B
A
P
P
A
B
B
P
B
P
P
B
A
B
M
F
F
F
M
M
M
M
M
M
F
M
M
F
M
F
F
M
M
M
74
67
72
63
62
74
66
70
83
77
69
67
77
65
75
70
68
70
67
80
16
28
50
27
42
4
19
28
1
29
12
23
1
29
21
13
27
22
10
21
No
No
No
No
No
No
No
No
Yes
Yes
No
No
Yes
No
Yes
Yes
Yes
No
No
Yes
P
B
B
A
P
A
B
A
B
P
B
A
B
P
A
A
P
A
P
A
F
F
F
F
F
F
M
M
F
F
F
M
F
M
F
M
M
M
F
F
67
77
76
69
64
72
59
69
69
79
65
76
69
60
67
75
68
65
72
69
30
16
9
18
1
25
29
1
42
20
14
25
24
26
11
6
11
15
11
3
No
No
Yes
Yes
Yes
No
No
No
No
Yes
No
Yes
No
Yes
No
Yes
Yes
No
Yes
No
The Neuralgia data set contains five variables. The Pain variable is the response. A specification of Pain=Yes
indicates that the patient felt pain, and Pain=No indicates that the patient did not feel pain. The variable
Treatment is a categorical variable with three levels: A and B represent the two test treatments, and P
represents the placebo treatment. The gender of the patients is given by the categorical variable Sex. The
variable Age is the age of the patients, in years, when treatment began. The duration of complaint, in
months, before the treatment began is given by the variable Duration.
In the following statements, a complex model that includes classification and continuous covariates and an
interaction term is fit to the Neuralgia data. When you try to create a default effect plot from this model,
computations stop because the best type of plot cannot easily be determined.
ods graphics on;
proc logistic data=Neuralgia;
class Treatment Sex / param=ref;
model Pain= Treatment|Sex Age Duration;
effectplot;
run;
ods graphics off;
434 F Chapter 19: Shared Concepts and Topics
To produce an effect plot for this model, you need to first choose the type of plot to be created. In this case,
since there are both classification and continuous covariates on the model, a SLICEFIT plot-type displays
the first continuous covariate (Age) on the X axis and displays fit curves that correspond to each level of the
first classification covariate (Treatment). The following statements produce Output 19.3.1.
ods graphics on;
proc logistic data=Neuralgia;
class Treatment Sex / param=ref;
model Pain= Treatment|Sex Age Duration;
effectplot slicefit;
run;
ods graphics off;
By default, effect plots from PROC LOGISTIC are displayed on the probability scale. The predicted values
are computed at the mean of the Duration variable, 16.73, and at the reference level of the Sex variable, M.
Observations are also displayed on the sliced-fit plot in Output 19.3.1. While the display of binary responses
can give you a feel for the spread of the data, it does not enable you to evaluate the fit of the model.
Output 19.3.1 Default Fit Plot Sliced by Treatment
Example 19.3: Logistic Regression F 435
In the following statements, an INTERACTION plot-type is specified for the Treatment variable, with the
Sex effect chosen for grouping the fits. The Age and Duration variables are set to their mean values for
computing the predicted values. The NOOBS option suppresses the display of the binary observations on
this plot. The LINK option is specified to display the fit on the LOGIT scale; if there is no interaction
between Treatment and Sex, then the resulting curves shown in Output 19.3.2 will have similar slopes
across the treatments.
ods graphics on;
proc logistic data=Neuralgia;
class Treatment Sex / param=ref;
model Pain= Treatment|Sex Age Duration;
effectplot interaction(x=Treatment sliceby=Sex) / noobs link;
run;
ods graphics off;
In Output 19.3.2, the slopes of the lines seem “parallel” across the treatments, corroborating the nonsignificance of the interaction terms.
Output 19.3.2 Interaction Plot of an Interaction Effect
436 F Chapter 19: Shared Concepts and Topics
In the following statements, the interaction effect is removed, and the Duration variable is investigated further. The PLOTBY(ROWS)= option displays the Sex levels in the rows of a panel of plots, and the AT
option computes the fits for several values of the Duration main effect in the columns of the panel. The
OBS(FRINGE) option moves the observations to a fringe (rug) plot at the bottom of the plot, the observations are subsetted and displayed according to the value of the PLOTBY= variable, and the JITTER option
makes overlaid fringes more visible. A STORE statement is also specified to save the model information
for a later display. These statements produce Output 19.3.3.
ods graphics on;
proc logistic data=Neuralgia;
class Treatment Sex / param=ref;
model Pain= Treatment Sex Age Duration;
effectplot slicefit(sliceby=Treatment plotby(rows)=Sex)
/ at(Duration=min midrange max) obs(fringe jitter(seed=39393));
store logimodel;
run;
ods graphics off;
The predicted probability curves in Output 19.3.3 look very similar across the different values of the Duration variable, which agrees with the nonsignificance of Duration in this model. The fringe plot displays only
female patients in the SEX=F row of the panel and displays only male patients in the SEX=M row, because
the PLOTBY=SEX option subsets the observations.
Output 19.3.3 Sliced-Fit Plot with AT Option
ESTIMATE Statement F 437
The following statements use the stored model and the PLM procedure to display a panel of contour plots:
ods graphics on;
proc plm restore=logimodel;
effectplot contour(plotby=Treatment) / at(Sex=all);
run;
ods graphics off;
Output 19.3.4 again confirms that Duration is not significant.
Output 19.3.4 Contour Fit Panel
ESTIMATE Statement
This statement documentation applies to the following SAS/STAT procedures:
LIFEREG, LOGISTIC, ORTHOREG, PHREG, PLM, PROBIT, QUANTREG, SURVEYLOGISTIC, SURVEYPHREG, and SURVEYREG. It also applies to the RELIABILITY procedure in SAS/QC software.
438 F Chapter 19: Shared Concepts and Topics
The ESTIMATE statement in the GENMOD, GLIMMIX, GLM, and MIXED procedures are documented
in the respective procedure chapters.
The ESTIMATE statement provides a mechanism for obtaining custom hypothesis tests. Estimates are
formed as linear estimable functions of the form Lˇ. You can perform hypothesis tests for the estimable
functions, construct confidence limits, and obtain specific nonlinear transformations.
Syntax: ESTIMATE Statement
ESTIMATE < ‘label’ > estimate-specification < (divisor =n) >
< , < ‘label’ > estimate-specification < (divisor =n) > > < , . . . >
< / options > ;
The basic element of the ESTIMATE statement is the estimate-specification, which consists of model effects
and their coefficients. A estimate-specification takes the general form
effect name < effect values . . . >
The following variables can appear in the ESTIMATE statement:
label
is an optional label that identifies the particular row of the estimate in the output.
effect
identifies an effect that appears in the MODEL statement. The keyword INTERCEPT
can be used as an effect when an intercept is fitted in the model. You do not need to
include all effects that are in the MODEL statement.
values
are constants that are elements of the L matrix and are associated with the fixed and
random effects. There are two basic methods of specifying the entries of the L matrix.
The traditional representation—also known as the positional syntax—relies on entering
coefficients in the position they assume in the L matrix. For example, in the following
statements the elements of L that are associated with the b main effect receive a 1 in the
first position and a –1 in the second position:
class a b;
model y = a b a*b;
estimate 'B at A2' b 1 -1
a*b 0
0
1 -1;
The elements that are associated with the interaction receive a 1 in the third position and a
–1 in the fourth position. In order to specify coefficients correctly for the interaction term,
you need to know how the levels of a and b vary in the interaction, which is governed by
the order of the variables in the CLASS statement. The nonpositional syntax is designed
to make it easier to enter coefficients for interactions and is necessary to enter coefficients
for effects that are constructed with the EFFECT statement. In square brackets you enter
the coefficient followed by the associated levels of the CLASS variables. If B has two
levels and A has three levels, the previous ESTIMATE statement, by using nonpositional
syntax for the interaction term, becomes the following statement:
Syntax: ESTIMATE Statement F 439
estimate 'B at A2' b 1 -1 a*b [1, 2 1] [-1, 2 2];
The previous statement assigns value 1 to the interaction where A is at level 2 and B
is at level 1, and it assigns –1 to the interaction where both classification variables are
at level 2. The comma that separates the entry for the L matrix from the level indicators is optional. Further details about the nonpositional contrast syntax and its use with
constructed effects can be found in the section “Positional and Nonpositional Syntax for
Coefficients in Linear Functions” on page 448.
Based on the estimate-specifications in your ESTIMATE statement, the procedure constructs the matrix L to
test the hypothesis H W Lˇ D 0. The procedure supports nonpositional syntax for the coefficients of model
effects in the ESTIMATE statement. For details see the section “Positional and Nonpositional Syntax for
Coefficients in Linear Functions” on page 448.
The procedure then produces for each row l of L an approximate t test of the hypothesis H W lˇ D 0. You can
also obtain multiplicity-adjusted p-values and confidence limits for multirow estimates with the ADJUST=
option.
Note that multirow estimates are permitted. Unlike releases prior to SAS 9.22, you do not need to specify a
‘label’ for every row of the estimate; the procedure constructs a default label if a label is not specified.
If the procedure finds the estimate to be nonestimable, then it displays “Non-est” for the estimate entry.
Table 19.18 summarizes important options in the ESTIMATE statement. All ESTIMATE options are subsequently discussed in alphabetical order.
Table 19.18
Option
ESTIMATE Statement Options
Description
Construction and Computation of Estimable Functions
DIVISOR=
Specifies a list of values to divide the coefficients
NOFILL
Suppresses the automatic fill-in of coefficients for higher-order effects
SINGULAR=
Tunes the estimability checking difference
Degrees of Freedom and p-values
ADJUST=
Determines the method for multiple comparison adjustment of estimates
ALPHA=˛
Determines the confidence level (1 ˛)
LOWER
Performs one-sided, lower-tailed inference
STEPDOWN
Adjusts multiplicity-corrected p-values further in a step-down
fashion
TESTVALUE=
Specifies values under the null hypothesis for tests
UPPER
Performs one-sided, upper-tailed inference
440 F Chapter 19: Shared Concepts and Topics
Table 19.18 continued
Option
Statistical Output
CL
CORR
COV
E
JOINT
PLOTS=
SEED=
Description
Constructs confidence limits
Displays the correlation matrix of estimates
Displays the covariance matrix of estimates
Prints the L matrix
Produces a joint F or chi-square test for the estimable functions
Requests ODS statistical graphics if the analysis is sampling-based
Specifies the seed for computations that depend on random
numbers
Generalized Linear Modeling
CATEGORY=
Specifies how to construct estimable functions with multinomial
data
EXP
Exponentiates and displays estimates
ILINK
Computes and displays estimates and standard errors on the inverse linked scale
You can specify the following options in the ESTIMATE statement after a slash (/).
ADJDFE=SOURCE
ADJDFE=ROW
specifies how denominator degrees of freedom are determined when p-values and confidence limits
are adjusted for multiple comparisons with the ADJUST= option. When you do not specify the
ADJDFE= option, or when you specify ADJDFE=SOURCE, the denominator degrees of freedom for
multiplicity-adjusted results are the denominator degrees of freedom for the final effect that is listed
in the ESTIMATE statement from the “Type III” table.
The ADJDFE=ROW setting is useful if you want multiplicity adjustments to take into account that
denominator degrees of freedom are not constant across estimates. For example, this can be the case
when the denominator degrees of freedom are computed by the Satterthwaite method or according to
Kenward and Roger (1997).
The ADJDFE= option has an effect only in mixed models that use these degree-of-freedom methods.
It is not supported by the procedures that perform chi-square-based inference (LOGISTIC, PHREG,
and SURVEYLOGISTIC).
ADJUST=BON
ADJUST=SCHEFFE
ADJUST=SIDAK
ADJUST=SIMULATE< (simoptions) >
ADJUST=T
requests a multiple comparison adjustment for the p-values and confidence limits for the estimates.
The adjusted quantities are produced in addition to the unadjusted quantities. Adjusted confidence
limits are produced if the CL or ALPHA= option is in effect. For a description of the adjustments,
Syntax: ESTIMATE Statement F 441
see Chapter 42, “The GLM Procedure,” and Chapter 61, “The MULTTEST Procedure,” and the documentation for the ADJUST= option in the LSMEANS statement.
If the STEPDOWN option is in effect, the p-values are further adjusted in a step-down fashion.
ALPHA=number
requests that a t type confidence interval be constructed with confidence level 1 – number. The value
of number must be between 0 and 1; the default is 0.05. If the “Estimates” table shows infinite degrees
of freedom, then the confidence interval is a z type interval.
CATEGORY=category-options
specifies how to construct estimates and multiplicity corrections for models with multinomial data
(ordinal or nominal). This option is also important for constructing sets of estimable functions for F
or chi-square tests with the JOINT option.
The category-options are used to indicate how response variable levels are treated in constructing the
estimable functions. Possible values for the category-options are the following:
JOINT
computes the estimable functions for every nonredundant category and treats them as a set. For
example, a three-row ESTIMATE statement in a model with three response categories leads to
six estimable functions.
SEPARATE
computes the estimable functions for every nonredundant category in turn. For example, a threerow ESTIMATE statement in a model with three response categories leads to two sets of three
estimable functions.
quoted-value-list
computes the estimable functions only for the list of values given. The list must consist of
formatted values of the response categories.
Consider the following ESTIMATE statements in the LOGISTIC procedure for an ordinal model with
response categories ‘vg’, ‘g’, ‘m’, ‘b’, and ‘vb’. Because there are five response categories, there are
four nonredundant categories for the cumulative link model.
proc logistic data=icecream;
class brand / param=glm;
model taste(order=data) = brand / link=logit;
freq count;
estimate brand 1 -1,
intercept 1 brand
estimate intercept 1 brand 1
estimate brand 1 -1,
brand 1 1 -2
run;
0 1 / category='m','vg';
/ category=joint
adjust=simulate(seed=1);
/ category=separate
adjust=bon;
442 F Chapter 19: Shared Concepts and Topics
The first ESTIMATE statement requests a two-row estimable function. The result is produced for
two of the four nonredundant response categories. The second ESTIMATE statement produces four t
tests, one for each nonredundant category. The multiplicity adjustment with p-value computation by
simulation treats the four estimable functions as a unit for family-wise Type I error protection. The
third ESTIMATE statement computes a two-row estimable function and reports its results separately
for all nonredundant categories. The Bonferroni adjustment in this statement applies to a family of
two tests that correspond to the two-row estimable function. Four Bonferroni adjustments for sets of
size two are performed.
The CATEGORY= option is supported only by the procedures that support generalized linear modeling (LOGISTIC and SURVEYLOGISTIC) and by PROC PLM when it is used to perform statistical
analyses on item stores created by these procedures.
CHISQ
requests that chi-square tests be performed in addition to F tests, when you request an F test with the
JOINT option. This option has no effect in procedures that produce chi-square statistics by default.
CL
requests that t type confidence limits be constructed. If the procedure shows the degrees of freedom
in the “Estimates” table as infinite, then the confidence limits are z intervals. The confidence level is
0.95 by default, and you can change the confidence level with the ALPHA= option. The confidence
intervals are adjusted for multiplicity when you specify the ADJUST= option. However, if a stepdown p-value adjustment is requested with the STEPDOWN option, only the p-values are adjusted
for multiplicity.
CORR
displays the estimated correlation matrix of the linear combination of the parameter estimates.
COV
displays the estimated covariance matrix of the linear combination of the parameter estimates.
DF=number
specifies the degrees of freedom for the t test and confidence limits. This option is not supported by the
procedures that perform chi-square-based inference (LOGISTIC, PHREG, and SUVEYLOGISTIC).
DIVISOR=value-list
specifies a list of values by which to divide the coefficients so that fractional coefficients can be
entered as integer numerators. If you do not specify value-list, a default value of 1.0 is assumed.
Missing values in the value-list are converted to 1.0.
If the number of elements in value-list exceeds the number of rows of the estimate, the extra values
are ignored. If the number of elements in value-list is less than the number of rows of the estimate,
the last value in value-list is copied forward.
If you specify a row-specific divisor as part of the specification of the estimate row, this value multiplies the corresponding divisor that is implied by the value-list. For example, the following statement
divides the coefficients in the first row by 8, and the coefficients in the third and fourth row by 3:
estimate 'One
'One
'One
'One
vs.
vs.
vs.
vs.
two'
three'
four'
five'
A
A
A
A
2 -2 (divisor=2),
1 0 -1
,
3 0 0 -3
,
1 0 0 0 -1 / divisor=4,.,3;
Coefficients in the second row are not altered.
Syntax: ESTIMATE Statement F 443
E
requests that the L matrix coefficients be displayed.
EXP
requests exponentiation of the estimate. When you model data with the logit, cumulative logit, or
generalized logit link functions, and the estimate represents a log odds ratio or log cumulative odds
ratio, the EXP option produces an odds ratio. In proportional hazards model, this option produces
estimates of hazard ratios. If you specify the CL or ALPHA= option, the (adjusted) confidence
bounds are also exponentiated.
The EXP option is supported only by PROC PHREG, PROC SURVEYPHREG, the procedures that
support generalized linear modeling (LOGISTIC and SURVEYLOGISTIC), and by PROC PLM
when it is used to perform statistical analyses on item stores created by these procedures.
ILINK
requests that the estimate and its standard error also be reported on the scale of the mean (the inverse
linked scale). The computation of the inverse linked estimate depends on the estimation mode. For
example, if the analysis is based on a posterior sample when a BAYES statement is present, the
inversely linked estimate is the average of the inversely linked values across the sample of posterior
parameter estimates. If the analysis is not based on a sample of parameter estimates, the procedure
computes the value on the mean scale by applying the inverse link to the estimate. The interpretation
of this quantity depends on the effect values specified in your ESTIMATE statement and on the link
function. For example, in a model for binary data with logit link the following statements compute
1
1 C expf .˛1
˛2 /g
where ˛1 and ˛2 are the fixed-effects solutions that are associated with the first two levels of the
classification effect A:
class A;
model y = A / dist=binary link=logit;
estimate 'A one vs. two' A 1 -1 / ilink;
This quantity is not the difference of the probabilities that are associated with the two levels,
1
2 D
1
1 C expf ˇ0
1
˛1 g
1 C expf ˇ0
˛2 g
The standard error of the inversely linked estimate is based on the delta method. If you also specify
the CL option, the procedure computes confidence limits for the estimate on the mean scale. In
multinomial models for nominal data, the limits are obtained by the delta method. In other models
they are obtained from the inverse link transformation of the confidence limits for the estimate. The
ILINK option is specific to an ESTIMATE statement.
The ILINK option is supported only by the procedures that support generalized linear modeling (LOGISTIC and SURVEYLOGISTIC) and by PROC PLM when it is used to perform statistical analyses
on item stores created by these procedures.
444 F Chapter 19: Shared Concepts and Topics
JOINT< (joint-test-options) >
requests that a joint F or chi-square test be produced for the rows of the estimate. The JOINT option
in the ESTIMATE statement essentially replaces the CONTRAST statement.
When the LOWERTAILED or the UPPERTAILED options are in effect, or if the BOUNDS option
described below is in effect, the JOINT option produces the chi-bar-square statistic according to
Silvapulle and Sen (2004). This statistic uses a simulation-based approach to compute p-values in
situations where the alternative hypotheses of the estimable functions are not simple two-sided hypotheses. See the section “Joint Hypothesis Tests with Complex Alternatives, the Chi-Bar-Square
Statistic” on page 451 for more information about this test statistic.
You can specify the following joint-test-options in parentheses:
ACC=
specifies the accuracy radius for determining the necessary sample size in the simulation-based
approach of Silvapulle and Sen (2004) for tests with order restrictions. The value of must be
strictly between 0 and 1; the default value is 0.005.
EPS=
specifies the accuracy confidence level for determining the necessary sample size in the
simulation-based approach of Silvapulle and Sen (2004) for tests with order restrictions. The
value of must be strictly between 0 and 1; the default value is 0.01.
LABEL=‘label’
assigns an identifying label to the joint test. If you do not specify a label, the first non-default
label for the ESTIMATE rows is used to label the joint test.
NOEST
ONLY
performs only the F or chi-square test and suppresses other results from the ESTIMATE statement. This option is useful for emulating the CONTRAST statement that is available in other
procedures.
NSAMP=n
specifies the number of samples for the simulation-based method of Silvapulle and Sen (2004).
If n is not specified, it is constructed from the values of the ALPHA=˛, the ACC=, and the
EPS= options. With the default values for , , and ˛ (0.005, 0.01, and 0.05, respectively),
NSAMP=12,604 by default.
CHISQ
adds a chi-square test if the procedure produces an F test by default.
BOUNDS=value-list
specifies boundary values for the estimable linear function. The null value of the hypothesis
is always zero. If you specify a positive boundary value z, the hypotheses are H W D 0,
Ha W W > 0 with the added constraint that < z. The same is true for negative boundary
values. The alternative hypothesis is then Ha W < 0 subject to the constraint > jzj. If
you specify a missing value, the hypothesis is assumed to be two-sided. The BOUNDS option
enables you to specify sets of one- and two-sided joint hypotheses. If all values in value-list are
set to missing, the procedure performs a simulation-based p-value calculation for a two-sided
test.
Syntax: ESTIMATE Statement F 445
LOWER
LOWERTAILED
requests that the p-value for the t test be based only on values that are less than the test statistic. A
two-tailed test is the default. A lower-tailed confidence limit is also produced if you specify the CL
or ALPHA= option.
Note that for ADJUST=SCHEFFE the one-sided adjusted confidence intervals and one-sided adjusted
p-values are the same as the corresponding two-sided statistics, because this adjustment is based on
only the right tail of the F distribution.
If you request a joint test with the JOINT option, then a one-sided left-tailed order restriction is applied
to all estimable functions, and the corresponding chi-bar-square statistic of Silvapulle and Sen (2004)
is computed in addition to the two-sided, standard, F or chi-square statistic. See the JOINT option for
how to control the computation of the simulation-based chi-bar-square statistic.
NOFILL
suppresses the automatic fill-in of coefficients of higher-order effects.
PLOTS=plot-options
produces ODS statistical graphics of the distribution of estimable functions if the procedure performs
the analysis in a sampling-based mode. For example, this is the case when procedures support a
BAYES statement and perform a Bayesian analysis. The estimable functions are then computed
for each of the posterior parameter estimates, and the “Estimates” table reports simple descriptive
statistics for the evaluated functions. The PLOTS= option enables you in this situation to visualize
the distribution of the estimable function. The following plot-options are available:
ALL
produces all possible plots with their default settings.
BOXPLOT< (boxplot-options) >
produces box plots of the distribution of the estimable function across the posterior sample. A
separate box is generated for each estimable function, and all boxes appear on a single graph by
default. You can affect the appearance of the box plot graph with the following options:
ORIENTATION=VERTICAL | HORIZONTAL
ORIENT=VERT | HORIZ
specifies the orientation of the boxes. The default is vertical orientation of the box plots.
NPANELPOS=number
specifies how to break the series of box plots across multiple panels. If the NPANELPOS
option is not specified, or if number equals zero, then all box plots are displayed in a single
graph; this is the default. If a negative number is specified, then exactly up to jnumber j
of box plots are displayed per panel. If number is positive, then the number of boxes per
panel is balanced to achieve small variation in the number of box plots per graph.
DISTPLOT< (distplot-options) >
DIST< (distplot-options) >
generates panels of histograms with a kernel density overlaid. A separate plot in each panel
contains the results for each estimable function. You can specify the following distplot-options
in parentheses:
446 F Chapter 19: Shared Concepts and Topics
BOX | NOBOX
controls the display of a horizontal box plot of the estimable function’s distribution across
the posterior sample below the graph. The BOX option is enabled by default.
HIST | NOHIST
controls the display of the histogram of the estimable function’s distribution across the
posterior sample. The HIST option is enabled by default.
NORMAL | NONORMAL
controls the display of a normal density estimate on the graph. The NONORMAL option
is enabled by default.
KERNEL | NOKERNEL
controls the display of a kernel density estimate on the graph. The KERNEL option is
enabled by default.
NROWS=number
specifies the highest number of rows in a panel. The default is 3.
NCOLS=number
specifies the highest number of columns in a panel. The default is 3.
UNPACK
unpacks the panel into separate graphics.
NONE
does not produce any plots.
SEED=number
specifies the seed for the sampling-based components of the computations for the ESTIMATE statement (for example, chi-bar-square statistics and simulated p-values). The value of number must be
an integer. The seed is used to start the pseudo-random number generator for the simulation. If you
do not specify a seed, or if you specify a value less than or equal to zero, the seed is generated from
reading the time of day from the computer clock. There could be multiple ESTIMATE statements
with SEED= specifications and there could be other statements that can supply a random number
seed. Since the procedure has only one random number stream, the initial seed is shown in the SAS
log.
SINGULAR=number
tunes the estimability checking. If v is a vector, define ABS(v) to be the largest absolute value of the
elements of v. If ABS(L LT) is greater than c*number for any row of L in the contrast, then Lˇ
is declared nonestimable. Here, T is the Hermite form matrix .X0 X/ X0 X, and c is ABS(L), except
when it equals 0, and then c is 1. The value for number must be between 0 and 1; the default is 1E–4.
STEPDOWN< (step-down-options) >
requests that multiplicity adjustments for the p-values of estimates be further adjusted in a step-down
fashion. Step-down methods increase the power of multiple testing procedures by taking advantage
of the fact that a p-value is never declared significant unless all smaller p-values are also declared
significant. The STEPDOWN adjustment combined with ADJUST=BON corresponds to the methods
of Holm (1979) and “Method 2” of Shaffer (1986); this is the default. Using step-down-adjusted pvalues combined with ADJUST=SIMULATE corresponds to the method of Westfall (1997).
Syntax: ESTIMATE Statement F 447
If the ESTIMATE statement is applied with a STEPDOWN option in a mixed model where the
degrees-of-freedom method is that of Kenward and Roger (1997) or of Satterthwaite, then step-downadjusted p-values are produced only if the ADJDFE=ROW option is in effect.
Also, the STEPDOWN option affects only p-values, not confidence limits.
For ADJUST=SIMULATE, the generalized least squares hybrid approach of Westfall (1997) is used to
increase Monte Carlo accuracy. You can specify the following step-down-options in parentheses after
the STEPDOWN option:
MAXTIME=n
specifies the time (in seconds) to be spent computing the maximal logically consistent sequential subsets of equality hypotheses for TYPE=LOGICAL. The default is MAXTIME=60. If the
MAXTIME value is exceeded, the adjusted tests are not computed. When this occurs, you can
try increasing the MAXTIME value. However, note that there are common multiple comparisons problems for which this computation requires a huge amount of time—for example, all
pairwise comparisons between more than 10 groups. In such cases, try to use TYPE=FREE (the
default) or TYPE=LOGICAL(n) for small n.
ORDER=PVALUE
ORDER=ROWS
specifies the order in which the step-down tests to be performed. ORDER=PVALUE is the
default, with estimates being declared significant only if all estimates with smaller (unadjusted)
p-values are significant. If you specify ORDER=ROWS, then significances are evaluated in the
order in which they are specified in the syntax.
REPORT
specifies that a report on the step-down adjustment be displayed, including a listing of the sequential subsets (Westfall 1997) and, for ADJUST=SIMULATE, the step-down simulation results.
TYPE=LOGICAL< (n) >
TYPE=FREE
specifies how step-down adjustment are made. If you specify TYPE=LOGICAL, the step-down
adjustments are computed by using maximal logically consistent sequential subsets of equality
hypotheses (Shaffer 1986; Westfall 1997). Alternatively, for TYPE=FREE, sequential subsets
are computed ignoring logical constraints. The TYPE=FREE results are more conservative than
those for TYPE=LOGICAL, but they can be much more efficient to produce for many estimates.
For example, it is not feasible to take logical constraints between all pairwise comparisons of
more than about 10 groups. For this reason, TYPE=FREE is the default.
However, you can reduce the computational complexity of taking logical constraints into account by limiting the depth of the search tree used to compute them, specifying the optional
depth parameter as a number n in parentheses after TYPE=LOGICAL. As with TYPE=FREE,
results for TYPE=LOGICAL(n) are conservative relative to the true TYPE=LOGICAL results.
But even for TYPE=LOGICAL(0) they can be appreciably less conservative than TYPE=FREE,
and they are computationally feasible for much larger numbers of estimates. If you do not specify n or if n = –1, the full search tree is used.
448 F Chapter 19: Shared Concepts and Topics
TESTVALUE=value-list
TESTMEAN=value-list
specifies the value under the null hypothesis for testing the estimable functions in the ESTIMATE
statement. The rules for specifying the value-list are very similar to those for specifying the divisor
list in the DIVISOR= option. If no TESTVALUE= is specified, all tests are performed as H W Lˇ D 0.
Missing values in the value-list also are translated to zeros. If you specify fewer values than rows in
the ESTIMATE statement, the last value in value-list is carried forward.
The TESTVALUE= option affects only p-values from individual, joint, and multiplicity-adjusted tests.
It does not affect confidence intervals.
The TESTVALUE option is not available for the multinomial distribution, and the values are ignored
when you perform a sampling-based (Bayesian) analysis.
UPPER
UPPERTAILED
requests that the p-value for the t test be based only on values that are greater than the test statistic. A
two-tailed test is the default. An upper-tailed confidence limit is also produced if you specify the CL
or ALPHA= option.
Note that for ADJUST=SCHEFFE the one-sided adjusted confidence intervals and one-sided adjusted
p-values are the same as the corresponding two-sided statistics, because this adjustment is based on
only the right tail of the F distribution.
If you request a joint test with the JOINT option, then a one-sided right-tailed order restriction is applied to all estimable functions, and the corresponding chi-bar-square statistic of
Silvapulle and Sen (2004) is computed in addition to the two-sided, standard, F or chi-square statistic. See the JOINT option for how to control the computation of the simulation-based chi-bar-square
statistic.
Positional and Nonpositional Syntax for Coefficients in Linear Functions
When you define custom linear hypotheses with the ESTIMATE statement, the procedure sets up an L
vector or matrix that conforms to the model effect solutions. (Note that the following remarks also apply to
the LSMESTIMATE statement, where you specify coefficients of the matrix K which is then converted into
a coefficient matrix that conforms to the model effects solutions.)
There are two methods for specifying the entries in a coefficient matrix (hereafter simply referred to as the
L matrix); they are called the positional and nonpositional methods. In the positional form, which is the
traditional method, you provide a list of values that occupy the elements of the L matrix that is associated
with the effect in question in the order in which the values are listed. For traditional model effects that consist
of continuous and classification variables, the positional syntax is simpler in some cases (main effects) and
more cumbersome in others (interactions). When you work with effects that are constructed through the
EFFECT statement, the nonpositional syntax is essential.
For example, consider the following two-way model with interactions where factors A and B have three and
two levels, respectively:
Positional and Nonpositional Syntax for Coefficients in Linear Functions F 449
proc logistic;
class a b;
model y = a b a*b;
run;
To test the difference of the B levels at the second level of A with an ESTIMATE statement (a slice), you
need to assign coefficients 1 and –1 to the levels of B and to the levels of the interaction where A is at
the second level. Two examples of equivalent ESTIMATE statements that use positional and nonpositional
syntax are as follows:
estimate 'B at A2' b 1 -1 a*b 0 0 1 -1
;
estimate 'B at A2' b 1 -1 a*b [1 2 1] [-1 2 2];
Because A precedes B in the CLASS statement, the levels of the interaction are formed as
˛1 ˇ1 ; ˛1 ˇ2 ; ˛2 ˇ1 ; ˛2 ˇ2 ; . If B precedes A in the CLASS statement, you need to modify the coefficients accordingly:
proc logistic;
class b a;
model y = a
estimate 'B
estimate 'B
estimate 'B
run;
b a*b;
at A2' b 1 -1 a*b 0 1 0 0 -1
;
at A2' b 1 -1 a*b [1 1 2] [-1 2 2];
at A2' b 1 -1 a*b [1, 1 2] [-1, 2 2];
You can optionally separate the L value entry from the level indicators with a comma, as in the last ESTIMATE statement.
The general syntax for defining coefficients with the nonpositional syntax is as follows:
effect-name [multiplier < , > level-values] . . . < [multiplier < , > level-values] >
The first entry in square brackets is the multiplier that is applied to the elements of L for the effect after the
level-values have been resolved and any necessary action that forms L has been taken.
The level-values are organized in a specific form:
The number of entries should equal the number of terms that are needed to construct the effect. For
effects that do not contain any constructed effects, this number is simply the number of terms in the
name of the effect.
Values of continuous variables that are needed for the construction of the L matrix precede the level
indicators of CLASS variables.
If the effect involves constructed effects, then you need to provide as many continuous and classification variables as are needed for the effect formation. For example, if a collection effect is defined
as
class c;
effect v = collection(x1 x2 c);
then a proper nonpositional syntax would be
450 F Chapter 19: Shared Concepts and Topics
v [0.5,
0.2 0.3 3]
If an effect contains both regular terms (old-style effects) and constructed effects, then the order
of the coefficients is as follows: continuous values for old-style effects, class levels for classification
variables in old-style effects, continuous values for constructed effects, and finally class levels that are
needed for constructed effects. Assume that C has four levels so that effect v contributes six elements
to the L matrix. When the procedure resolves this syntax, the values 0.2 and 0.3 are assigned to the
positions for x1 and x2 and a 1 is associated with the third level of C. The resulting vector is then
multiplied by 0.5 to produce
Œ0:1
0:15
0
0
0:5
0
Note that you enter the levels of the classification variables in the square brackets, not their formatted values.
The ordering of the levels of classification variables can be gleaned from the “Class Level Information”
table.
To specify values for continuous variables, simply give their value as one of the terms in the effect. The
nonpositional syntax in the following ESTIMATE statement is read as “1 times the value 0.4 in the column
that is associated with level 2 of A”
proc phreg;
class a / param=glm;
model y = a a*x / s;
lsmeans a / e at x=0.4;
estimate 'A2 at x=0.4' intercept 1 a 0 1 a*x [1,0.4 2] / e;
run;
Because the value before the comma serves as a multiplier, the same estimable function could also be
constructed with the following statements:
estimate 'A2 at x=0.4' intercept 1 a 0 1 a*x [ 4, 0.1 2];
estimate 'A2 at x=0.4' intercept 1 a 0 1 a*x [ 2, 0.2 2];
estimate 'A2 at x=0.4' intercept 1 a 0 1 a*x [-1, -0.4 2];
Note that continuous variables that are needed to construct an effect are always listed before any CLASS
variables.
When you work with constructed effects, the nonpositional syntax works in the same way. For example,
the following model contains a classification effect and a B-spline. The first two ESTIMATE statements
produce predicted values for level 1 of C when the continuous variable x takes on the values 20 and 10,
respectively.
proc orthoreg;
class c;
effect spl = spline(x /
model y = c spl;
estimate 'C = 1 @ x=20'
'C = 1 @ x=10'
estimate 'Difference'
run;
knotmethod=equal(5));
intercept 1 c 1 spl [1,20],
intercept 1 c 1 spl [1,10];
spl [1,20] [-1,10];
Joint Hypothesis Tests with Complex Alternatives, the Chi-Bar-Square Statistic F 451
In this example, the ORTHOREG procedure computes the spline coefficients for the first ESTIMATE statement based on x = 20, and similarly in the second statement for x = 10. The third ESTIMATE statement
computes the difference of the predicted values. Because the spline effect does not interact with the classification variable, this difference does not depend on the level of C. If such an interaction is present, you can
estimate the difference in predicted values for a given level of C by using the nonpositional syntax. Because
the effect C*spl contains both old-style terms (C) and a constructed effect, you specify the values for the
old-style terms before assigning values to constructed effects.
proc orthoreg;
class c;
effect spl = spline(x / knotmethod=equal(5));
model y = spl*c;
estimate 'C2 = 1, x=20' intercept 1 c*spl [1,1 20];
estimate 'C2 = 2, x=20' intercept 1 c*spl [1,2 20];
estimate 'C diff at x=20' c*spl [1,1 20] [-1,2 20];
run;
It is recommended that you add the E option to the ESTIMATE or LSMESTIMATE statement to verify that
the L matrix is formed according to your expectations.
In any row of an ESTIMATE statement you can choose positional and nonpositional syntax separately for
each effect. However, you cannot mix the two forms of syntax for coefficients of a single effect. For
example, the following statement is not proper because both forms of syntax are used for the interaction
effect:
estimate 'A1B1 - A1B2' b 1 -1
a*b 0 1
[-1, 1 2];
Joint Hypothesis Tests with Complex Alternatives, the Chi-Bar-Square
Statistic
Silvapulle and Sen (2004) propose a test statistic for testing hypotheses where the null or the alternative
hypothesis or both involve inequalities. You can test special cases of these hypotheses with the JOINT
option in the ESTIMATE and the LSMESTIMATE statement. Consider the k estimable functions Lˇ and
the hypotheses H0 W Lˇ D 0 and Ha W Lˇ 0. The alternative hypothesis defines a convex cone C at the
origin. Suppose that under the null hypothesis Lb̌ follows a multivariate normal distribution with mean 0
and variance V. The restricted alternative prevents you from using the usual F or chi-square test machinery,
since the distribution of the test statistic under the alternative might not follow the usual rules. Silvapulle and
Sen (2004) coined a statistic that takes into account the projection of the observed estimate onto the convex
cone formed by the alternative parameter space. This test statistic is called the chi-bar-square statistic, and
p-values are obtained by simulation; see, in particular, Chapter 3.4 in Silvapulle and Sen (2004).
Briefly, let U be a multivariate normal random variable with mean 0 and variance matrix V. The chi-barsquare statistic is the random variable
2 D U0 V
1
U
Q D min.U
2C
Q
/0 V
1
.U
/
and it can be motivated by a geometric argument. The quadratic form in Q is the V-projection of U onto
Q If U 2 C, then Q = 0 and U
Q D U. If U is completely
the cone C. Suppose that this projected point is U.
452 F Chapter 19: Shared Concepts and Topics
Q is a point on the surface of the cone. Similarly, U0 V 1 U is the length of the
outside of the cone C, then U
segment from the origin to U in the V-space with norm jjxjj D .x0 V 1 x/1=2 . If you apply the Pythagorean
theorem, you can see that the chi-bar-square statistic measures the length of the segment from the origin to
Q in C.
the projected point U
To calculate p-values for chi-bar-square statistics, a simulation-based approach is taken. Consider again the
O 0 D V.
set of k estimable functions Lˇ with estimate Lb̌ D U and variance LVarŒˇL
First, the observed value of the statistic is computed as
2obs D U0 V
1
Q
U
Then, n independent random samples Z1 ; ; Zn are drawn from an N.0; V/ distribution and the following
chi-bar-statistics are computed for the sample:
21 D Z01 V
1
Z1
min.Z1
/0 V
1
min.Zn
/0 V
1
2C
.Z1
/
::
:
2n D Z0n V
1
Zn
2C
.Zn
/
The p-value is estimated by the fraction of simulated statistics that are greater than or equal to the observed
value 2obs .
Notice that unless U is interior to the cone C, finding the value of Q requires the solution to a quadratic
optimization problem. When k is large, or when many simulations are requested, the computation of pvalues for chi-bar-square statistics might require considerable computing time.
ODS Table Names: ESTIMATE Statement
Each table created by the ESTIMATE statement has a name associated with it, and you can use this name
to refer to the table when you use the Output Delivery System (ODS) to select tables and create output data
sets. These names are listed in Table 19.19. For more information about ODS, see Chapter 20, “Using the
Output Delivery System.”
Table 19.19 ODS Tables Produced by the ESTIMATE statement
Table Name
Description
Required Option
Coef
Estimates
Contrasts
L matrix coefficients
ESTIMATE statement results
Joint test results
E
Default
JOINT
ODS Graphics: ESTIMATE Statement
This section describes the use of ODS Graphics for creating statistical graphs of the distribution of estimable
functions with the ESTIMATE statement. The plots can be produced only in association with the LIFEREG
LSMEANS Statement F 453
and PHREG procedures, which can perform Bayesian analysis. The plots are available via these procedures
directly, and also via PROC PLM when it is run using an item store that was created by these procedures.
To request these graphs you must do the following:
ensure that ODS Graphics is enabled
use a BAYES statement with PROC LIFEREG or PROC PHREG, or use PROC PLM to perform
statistical analysis on an item store that was saved from a Bayesian analysis
request plots with the PLOTS= option in the ESTIMATE statement
For more information about ODS Graphics, see Chapter 21, “Statistical Graphics Using ODS.” The available
graphs are summarized in Table 19.20.
Table 19.20 Graphs Produced by the ESTIMATE statement
ODS Graph Name
Plot Description
Required Option
BoxPlot
Displays box plots of estimable functions across a posterior sample.
Displays panels of histograms with
kernel density curves overlaid. Each
plot contains the results for the posterior sample of each estimable function.
Displays a histogram with a kernel
density curve overlaid. The plot contains the results for the posterior sample of the estimable function.
PLOTS=BOXPLOT
DistPanel
DistPlot
PLOTS=DISTPLOT
PLOTS=DISTPLOT(UNPACK)
For details about the plot-options of the ESTIMATE statement, see the PLOTS= option in the section “ESTIMATE Statement” on page 437.
LSMEANS Statement
This statement documentation applies to the following procedures:
GENMOD, LIFEREG, LOGISTIC, ORTHOREG, PHREG, PLM, PROBIT, SURVEYLOGISTIC, SURVEYPHREG, and SURVEYREG. It also applies to the RELIABILITY procedure in SAS/QC software.
The GLIMMIX, GLM, and MIXED procedures also support LSMEANS statements. The relevant statement
documentation for these procedures can be found in the specific procedure chapter.
The LSMEANS statement computes least squares means (LS-means) of fixed effects. In the GLM, MIXED,
and GLIMMIX procedures, LS-means are predicted population margins—that is, they estimate the marginal
454 F Chapter 19: Shared Concepts and Topics
means over a balanced population. In a sense, LS-means are to unbalanced designs as class and subclass
arithmetic means are to balanced designs.
Thus it is important not to interpret the name with a strict association with least squares estimation. Least
squares is the predominant estimation technique for the type of models in which LS-means were first applied. Their interpretation and importance reaches beyond the least squares principle, however. A more
appropriate approach to LS-means views them as linear combinations of the parameter estimates that are
constructed in such a way that they correspond to average predicted values in a population where the levels
of classification variables are balanced.
This contemporary—and historically correct—interpretation of the concept of least squares means underlines their importance in all classes of models where predicted values are reasonably formed as linear combinations of the parameter estimates. LS-means distinguish themselves from general estimable functions
in that they take the structure for the model and data into account through the structure of the X and X0 X
matrix in your model. For example, in a generalized linear model the structure of the X matrix informs the
analysis about the possible levels of classification variables and predictions on the linear (the linked) scale
are computed as x0 ˇ. LS-means are thus meaningful quantities in such models when the linear estimable
function that corresponds to an averaged prediction is constructed on the linked scale. For example, in a
binomial model with logit link, the least squares means are predicted population margins of the logits. You
can then transform the least squares means to the data scale with the ILINK option, and you can display
differences of least squares means in terms of odds ratios with the ODDSRATIO option. The underlying
principle—unless you perform a Bayesian analysis—is to construct the estimates or their differences on the
linked scale and to apply appropriate transformations in a second step.
Least squares means computations are also supported for multinomial models.
LS-means are computed as Lˇ where the L matrix that is constructed to compute the predicted values is the
same as the L matrix that is formed in PROC GLM.
Each LS-mean is computed as Lb̌, where L is the coefficient matrix that is associated with the least squares
mean and b̌ is the estimate of the fixed-effects parameter vector. The approximate standard error for the
LS-mean is computed as the square root of LVarŒb̌L0 . The approximate variance matrix of the fixed-effects
estimates depends on the estimation method.
b
Syntax: LSMEANS Statement
LSMEANS < model-effects > < / options > ;
LS-means can be computed for any effect in the statistical model that involves only CLASS variables. You
can specify multiple effects in one LSMEANS statement or in multiple LSMEANS statements, and all
LSMEANS statements must appear after the MODEL statement. If you do not specify model-effects, the
options in the LSMEANS statement are applied to all suitable model effects.
As in the ESTIMATE statement, the L matrix is tested for estimability; if this test fails, the procedure
displays “Non-est” for the LS-means entries. Note that linear functions of LS-means, such as differences,
can be estimable, even if the means themselves are not estimable. Estimability checks for differences are
thus applied separately from checks for the means.
Assuming the LS-mean is estimable, the procedure constructs an approximate t test to test the null hypothesis that the associated population quantity equals zero.
Syntax: LSMEANS Statement F 455
Table 19.21 summarizes important options in the LSMEANS statement. All LSMEANS options are subsequently discussed in alphabetical order.
Table 19.21
Option
LSMEANS Statement Options
Description
Construction and Computation of LS-Means
AT
Modifies the covariate value in computing LS-means
BYLEVEL
Computes separate margins
DIFF
Requests differences of LS-means
OM=
Specifies the weighting scheme for LS-means computation as determined by the input data set
SINGULAR=
Tunes estimability checking
Degrees of Freedom and p-values
ADJUST=
Determines the method for multiple-comparison adjustment of LSmeans differences
ALPHA=˛
Determines the confidence level (1 ˛)
STEPDOWN
Adjusts multiple-comparison p-values further in a step-down
fashion
Statistical Output
CL
CORR
COV
E
LINES
MEANS
PLOTS=
SEED=
Constructs confidence limits for means and mean differences
Displays the correlation matrix of LS-means
Displays the covariance matrix of LS-means
Prints the L matrix
Produces a “Lines” display for pairwise LS-means differences
Prints the LS-means
Requests graphs of means and mean comparisons
Specifies the seed for computations that depend on random
numbers
Generalized Linear Modeling
EXP
Exponentiates and displays estimates of LS-means or LS-means
differences
ILINK
Computes and displays estimates and standard errors of LS-means
(but not differences) on the inverse linked scale
ODDSRATIO
Reports (simple) differences of least squares means in terms of
odds ratios if permitted by the link function
You can specify the following options in the LSMEANS statement after a slash (/):
ADJDFE=ROW
ADJDFE=SOURCE
specifies how denominator degrees of freedom are determined when p-values and confidence limits
are adjusted for multiple comparisons with the ADJUST= option. When you do not specify the
ADJDFE= option or when you specify ADJDFE=SOURCE, the denominator degrees of freedom for
456 F Chapter 19: Shared Concepts and Topics
multiplicity-adjusted results are the denominator degrees of freedom for the LS-mean effect in the
“Type III Tests of Fixed Effects” table. When you specify ADJDFE=ROW, the denominator degrees
of freedom for multiplicity-adjusted results correspond to the degrees of freedom that are displayed
in the DF column of the “Differences of Least Squares Means” table.
The ADJDFE=ROW setting is particularly useful if you want multiplicity adjustments to take into
account that denominator degrees of freedom are not constant across LS-mean differences.
In one-way models with heterogeneous variance, combining certain ADJUST= options with the ADJDFE=ROW option corresponds to particular methods of performing multiplicity adjustments in the
presence of heteroscedasticity. For example, the following statements fit a heteroscedastic one-way
model and perform Dunnett’s T3 method (Dunnett 1980), which is based on the studentized maximum
modulus (ADJUST=SMM):
proc glimmix;
class A;
model y = A / ddfm=satterth;
random _residual_ / group=A;
lsmeans A / adjust=smm adjdfe=row;
run;
If you combine the ADJDFE=ROW option with ADJUST=SIDAK, the multiplicity adjustment corresponds to the T2 method of Tamhane (1979), and ADJUST=TUKEY corresponds to the method of
Games-Howell (Games and Howell 1976). Note that ADJUST=TUKEY gives the exact results for the
case of fractional degrees of freedom in the one-way model, but it does not take into account that the
degrees of freedom are subject to variability. A more conservative method, such as ADJUST=SMM,
might protect the overall error rate better.
Unless the ADJUST= option is specified in the LSMEANS statement, the ADJDFE= option has
no effect. The option is not supported by the procedures that perform chi-square-based inference
(GENMOD, LOGISTIC, PHREG, and SURVEYLOGISTIC).
ADJUST=BON
ADJUST=DUNNETT
ADJUST=NELSON
ADJUST=SCHEFFE
ADJUST=SIDAK
ADJUST=SIMULATE< (simoptions) >
ADJUST=SMM | GT2
ADJUST=TUKEY
requests a multiple comparison adjustment for the p-values and confidence limits for the differences of
LS-means. The adjusted quantities are produced in addition to the unadjusted quantities. By default,
the procedure performs all pairwise differences. If you specify ADJUST=DUNNETT, the procedure
analyzes all differences with a control level. If you specify ADJUST=NELSON, ANOM differences
are taken. The ADJUST= option implies the DIFF option.
The BON (Bonferroni) and SIDAK adjustments involve correction factors described in Chapter 42,
“The GLM Procedure,” and Chapter 61, “The MULTTEST Procedure”; also see Westfall and Young
Syntax: LSMEANS Statement F 457
(1993) and Westfall et al. (1999). When you specify ADJUST=TUKEY and your data are unbalanced, the procedure uses the approximation described in Kramer (1956) and identifies the adjustment as “Tukey-Kramer” in the results. Similarly, when you specify ADJUST=DUNNETT or ADJUST=NELSON and the LS-means are correlated, the procedure uses the factor-analytic covariance
approximation described in Hsu (1992) and identifies the adjustment in the results as “Dunnett-Hsu”
or “Nelson-Hsu,” respectively. The approximation derives an approximate “effective sample sizes”
for which exact critical values are computed. Computing the exact adjusted p-values and critical values for unbalanced designs can be computationally intensive, in particular for ADJUST=NELSON.
A simulation-based approach, as specified by the ADJUST=SIM option, while nondeterministic, can
provide inferences that are sufficiently accurate in much less time. The preceding references also
describe the SCHEFFE and SMM adjustments.
Nelson’s adjustment applies only to the analysis of means (Ott 1967; Nelson 1982, 1991, 1993), where
LS-means are compared against an average LS-mean. It does not apply to all pairwise differences of
least squares means. See the DIFF=ANOM option for more details regarding the analysis of means
with the procedure.
The SIMULATE adjustment computes adjusted p-values and confidence limits from the simulated
distribution of the maximum or maximum absolute value of a multivariate t random vector. All covariance parameters, except the residual scale parameter, are fixed at their estimated values throughout the simulation, potentially resulting in some underdispersion. The simulation estimates q, the true
.1 ˛/ quantile, where 1 ˛ is the confidence coefficient. The default ˛ is 0.05, and you can change
this value with the ALPHA= option in the LSMEANS statement.
The number of samples is set so that the tail area for the simulated q is within of 1
100.1 /% confidence. In equation form,
Pr.jF .b
q/
.1
˛/j / D 1
˛ with
where qO is the simulated q and F is the true distribution function of the maximum; see Edwards
and Berry (1987) for details. By default, = 0.005 and = 0.01, placing the tail area of qO within
0.005 of 0.95 with 99% confidence. You can specify the following simoptions in parentheses after
the ADJUST=SIMULATE option:
ACC=value
specifies the target accuracy radius of a 100.1 /% confidence interval for the true probability
content of the estimated .1 ˛/ quantile. The default value is ACC=0.005.
EPS=value
specifies the value for a 100 .1 /% confidence interval for the true probability content
of the estimated .1 ˛/ quantile. The default value for the accuracy confidence is 99%, which
corresponds to EPS=0.01.
NSAMP=n
specifies the sample size for the simulation. By default, n is set based on the values of the target
accuracy radius and accuracy confidence 100 .1 /% for an interval for the true probability
content of the estimated .1 ˛/ quantile. With the default values for , , and ˛ (0.005, 0.01,
and 0.05, respectively), NSAMP=12,604 by default.
458 F Chapter 19: Shared Concepts and Topics
SEED=number
specifies an integer that is used to start the pseudo-random number generator for the simulation.
If you do not specify a seed, or specify a value less than or equal to zero, the seed is by default
generated from reading the time of day from the computer’s clock.
THREADS
specifies that the computational work for the simulation be divided into parallel threads, where
the number of threads is the value of the SAS system option CPUCOUNT=. For large simulations (as specified directly using the NSAMP= simoption or indirectly using the ACC= or
EPS= simoptions), parallel processing can markedly speed up the computation of adjusted pvalues and confidence intervals. However, because the parallel processing has different pseudorandom number streams, the precise results are different from the default ones, which are
computed in sequence rather than in parallel. This option overrides the SAS system option
THREADS | NOTHREADS.
NOTHREADS
specifies that the computational work for the simulation be performed in sequence rather
than in parallel. NOTHREADS is the default. This option overrides the SAS system option
THREADS | NOTHREADS.
If the STEPDOWN option is in effect, the p-values are further adjusted in a step-down fashion. For
certain options and data, this adjustment is exact under an iid N.0; 2 / model for the dependent
variable, in particular for the following:
for ADJUST=DUNNETT when the means are uncorrelated
for ADJUST=TUKEY with STEPDOWN(TYPE=LOGICAL) when the means are balanced and
uncorrelated.
The first case is a consequence of the nature of the successive step-down hypotheses for comparisons with a control; the second uses an extension of the maximum studentized range distribution
appropriate for partition hypotheses (Royen 1989). Finally, for STEPDOWN(TYPE=FREE), ADJUST=TUKEY employs the Royen (1989) extension in such a way that the resulting p-values are
conservative.
ALPHA=number
requests that a t type confidence interval be constructed for each of the LS-means with confidence
level 1 – number. The value of number must be between 0 and 1; the default is 0.05.
AT variable=value
AT (variable-list)=(value-list)
AT MEANS
modifies the values of the covariates that are used in computing LS-means. By default, all covariate
effects are set equal to their mean values for computation of standard LS-means. The AT option
enables you to assign arbitrary values to the covariates. Additional columns in the output table indicate
the values of the covariates.
If there is an effect that contains two or more covariates, the AT option sets the effect equal to the
product of the individual means rather than the mean of the product (as with standard LS-means
calculations). The AT MEANS option sets covariates equal to their mean values (as with standard
LS-means) and incorporates this adjustment to crossproducts of covariates.
Syntax: LSMEANS Statement F 459
As an example, consider the following statements:
class A;
model Y = A
lsmeans A;
lsmeans A /
lsmeans A /
lsmeans A /
x1 x2 x1*x2;
at means;
at x1=1.2;
at (x1 x2)=(1.2 0.3);
For the first two LSMEANS statements, the LS-means coefficient for x1 is x 1 (the mean of x1) and
for x2 is x 2 (the mean of x2). However, for the first LSMEANS statement, the coefficient for x1*x2
is x1 x2 , but for the second LSMEANS statement, the coefficient is x 1 x 2 . The third LSMEANS
statement sets the coefficient for x1 equal to 1.2 and leaves it at x 2 for x2, and the final LSMEANS
statement sets these values to 1.2 and 0.3, respectively.
Even if you specify a WEIGHT variable, the unweighted covariate means are used for the covariate
coefficients if there is no AT specification. If you specify the AT option, WEIGHT or FREQ variables
are taken into account as follows. The weighted covariate means are then used for the covariate
coefficients for which no explicit AT values are given, or if you specify AT MEANS. Observations that
do not contribute to the analysis because of a missing dependent variable are included in computing
the covariate means. Use the E option in conjunction with the AT option to check that the modified
LS-means coefficients are the ones you want.
The AT option is disabled if you specify the BYLEVEL option.
BYLEVEL
requests that separate margins be computed for each level of the LSMEANS effect.
The standard LS-means have equal coefficients across classification effects. The BYLEVEL option
changes these coefficients to be proportional to the observed margins. This adjustment is reasonable
when you want your inferences to apply to a population that is not necessarily balanced but has the
margins observed in the input data set. In this case, the resulting LS-means are actually equal to
raw means for fixed-effects models and certain balanced random-effects models, but their estimated
standard errors account for the covariance structure that you have specified. If a WEIGHT statement
is specified, the procedure uses weighted margins to construct the LS-means coefficients.
If the AT option is specified, the BYLEVEL option disables it.
CL
requests that t type confidence limits be constructed for each of the LS-means. The confidence level
is 0.95 by default; this can be changed with the ALPHA= option. If you specify an ADJUST= option,
then the confidence limits are adjusted for multiplicity. But if you also specify STEPDOWN, then
only p-values are step-down adjusted, not the confidence limits.
CORR
displays the estimated correlation matrix of the least squares means as part of the “Least Squares
Means” table.
COV
displays the estimated covariance matrix of the least squares means as part of the “Least Squares
Means” table.
460 F Chapter 19: Shared Concepts and Topics
DF=number
specifies the degrees of freedom for the t test and confidence limits. The default is the denominator
degrees of freedom taken from the “Type III Tests” table that corresponds to the LS-means effect.
The option is not supported by the procedures that perform chi-square-based inference (GENMOD,
LOGISTIC, PHREG and SURVEYLOGISTIC).
DIFF< =difftype >
PDIFF< =difftype >
requests that differences of the LS-means be displayed. You can use one of the following optional
difftype values to specify which differences to produce:
ALL
requests all pairwise differences; this is the default.
ANOM
requests differences between each LS-mean and the average LS-mean, as in the analysis of
means (Ott 1967). The average is computed as a weighted mean ofthe LS-means, the weights
being inversely proportional to the diagonal entries of the L X0 X L0 matrix. If LS-means
are nonestimable, this design-based weighted mean is replaced with an equally weighted mean.
Note that the ANOM procedure in SAS/QC software implements both tables and graphics for the
analysis of means with a variety of response types. For one-way designs and normal data with
identity link, the DIFF=ANOM computations are equivalent to the results of PROC ANOM. If
the LS-means being compared are uncorrelated, exact adjusted p-values and critical values for
confidence limits can be computed in the analysis of means; see Nelson (1982, 1991, 1993) and
Guirguis and Tobias (2004) in addition to the documentation for the ADJUST=NELSON option.
CONTROL
requests differences with a control, which, by default, is the first valid level of each of the specified LSMEANS effects. For example, suppose the effects A and B are classification variables,
both of them have two levels 1 and 2, and the A=1, B=1 cell is missing. Unless the procedure
supports a MISSING option in the CLASS statement and the option is in effect, the following
LSMEANS statement uses the level (1,2) of A*B as the control:
lsmeans A*B / diff=control;
Nevertheless, you can still specify a valid level as the control—for example, (2,1) of A*B. To
specify which levels of the effects are the controls, list the quoted formatted values in parentheses
after the CONTROL keyword. For example, if the effects A, B, and C are classification variables,
each having two levels, 1 and 2, the following LSMEANS statement specifies the (1,2) level of
A*B and the (2,1) level of B*C as controls:
lsmeans A*B B*C / diff=control('1' '2' '2' '1');
For multiple effects, the results depend upon the order of the list, and so you should check the
output to make sure that the controls are correct.
Two-tailed tests and confidence limits are associated with the CONTROL difftype. For onetailed results, use either the CONTROLL or CONTROLU difftype.
Syntax: LSMEANS Statement F 461
CONTROLL
tests whether the noncontrol levels are significantly smaller than the control; the upper confidence limits for the control minus the noncontrol levels are considered to be infinity and are
displayed as missing.
CONTROLU
tests whether the noncontrol levels are significantly larger than the control; the upper confidence
limits for the noncontrol levels minus the control are considered to be infinity and are displayed
as missing.
If you want to perform multiple comparison adjustments on the differences of LS-means, you must
specify the ADJUST= option.
The differences of the LS-means are displayed in a table titled “Differences of Least Squares Means.”
E
requests that the L matrix coefficients for the LSMEANS effects be displayed.
EXP
requests exponentiation of the LS-means or LS-mean differences. When you model data with the
logit, cumulative logit, or generalized logit link functions, and the estimate represents a log odds ratio
or log cumulative odds ratio, the EXP option produces an odds ratio. In proportional hazards model,
the exponentiation of the LS-mean differences produces estimates of hazard ratios. If you specify the
CL or ALPHA= option, the (adjusted) confidence bounds are also exponentiated.
The EXP option is supported only by PROC PHREG, PROC SURVEYPHREG, the procedures that
support generalized linear modeling (GENMOD, LOGISTIC, and SURVEYLOGISTIC), and PROC
PLM when it is used to perform statistical analyses on item stores that are created by these procedures.
ILINK
requests that estimates and their standard errors in the “Least Squares Means” table also be reported
on the scale of the mean (the inverse linked scale). This enables you to obtain estimates of predicted
probabilities and their standard errors in logistic models, for example. The option is specific to an
LSMEANS statement. If you also specify the CL option, the procedure computes confidence intervals
for the predicted means by applying the inverse link transform to the confidence limits on the linked
(linear) scale. Standard errors on the inverse linked scale are computed by the delta method.
The ILINK option is supported only by the procedures that support generalized linear modeling
(GENMOD, LOGISTIC and SURVEYLOGISTIC) and by PROC PLM when it is used to perform
statistical analyses on item stores that are created by these procedures.
LINES
presents results of comparisons between all pairs of least squares means by listing the means in
descending order and indicating nonsignificant subsets by line segments beside the corresponding
LS-means. When all differences have the same variance, these comparison lines are guaranteed to
accurately reflect the inferences that are based on the corresponding tests, which are made by comparing the respective p-values to the value of the ALPHA= option (0.05 by default). However, equal
variances might not be the case for differences between LS-means. If the variances are not all the
same, then the comparison lines might be conservative, in the sense that if you base your inferences
on the lines alone, you will detect fewer significant differences than the tests indicate. If there are any
such differences, the procedure lists the pairs of means that are inferred to be significantly different
462 F Chapter 19: Shared Concepts and Topics
by the tests but not by the comparison lines. However, even though the variances in many cases are
unequal, they are similar enough that the comparison lines accurately reflect the test inferences.
MEANS | NOMEANS
determines whether to print the least squares means themselves. For most procedure, MEANS is the
default behavior. For example, the NOMEANS option is the default for the PHREG procedure. You
can then use the MEANS option to produce the table of least squares means, if desired.
ODDSRATIO
OR
requests that LS-mean differences (DIFF, ADJUST= options) are also reported in terms of odds ratios.
The ODDSRATIO option is ignored unless you use either the logit, cumulative logit, or generalized
logit link function. If you specify the CL or ALPHA= option, confidence intervals for the odds ratios
are also computed. These intervals are adjusted for multiplicity when you specify the ADJUST=
option.
The ODDSRATIO option is supported only by the procedures that support generalized linear modeling (GENMOD, LOGISTIC and SURVEYLOGISTIC) and by PROC PLM when it is used to perform
statistical analyses on item stores created by these procedures.
OBSMARGINS< =OM-data-set >
OM< =OM-data-set >
specifies a potentially different weighting scheme for the computation of LS-means coefficients. The
standard LS-means have equal coefficients across classification effects; however, the OM option
changes these coefficients to be proportional to those found in the OM-data-set. This adjustment
is reasonable when you want your inferences to apply to a population that is not necessarily balanced
but has the margins that are observed in OM-data-set.
By default, OM-data-set is the same as the analysis data set. You can optionally specify another data
set that describes the population for which you want to make inferences. This data set must contain
all model variables except for the dependent variable (which is ignored if it is present). In addition,
the levels of all CLASS variables must be the same as those that occur in the analysis data set. If a
level of a classification effect in the original data set is not present in the OM-data-set, the LS-means
for that level are undefined. The corresponding rows of the LSMeans table are displayed as missing.
Specifying an OM-data-set enables you to construct arbitrarily weighted LS-means.
In computing the observed margins, the procedure uses all observations for which there are no missing
or invalid independent variables, including those for which there are missing dependent variables.
Also, if you use a WEIGHT statement, the procedure computes weighted margins to construct the
LS-means coefficients. If your data are balanced, the LS-means are unchanged by the OM option.
The BYLEVEL option modifies the observed-margins LS-means. Instead of computing the margins across all of the OM-data-set, the procedure computes separate margins for each level of the
LSMEANS effect in question. In this case the resulting LS-means are actually equal to raw means for
fixed-effects models and certain balanced random-effects models, but their estimated standard errors
account for the covariance structure that you have specified.
You can use the E option in conjunction with either the OM or BYLEVEL option to verify that the
modified LS-means coefficients are the ones you want. It is possible that the modified LS-means are
not estimable when the standard ones are estimable, or vice versa.
Syntax: LSMEANS Statement F 463
PDIFF
is the same as the DIFF option.
PLOT | PLOTS< =plot-request< (options) > >
PLOT | PLOTS< =(plot-request< (options) > < . . . plot-request< (options) > >) >
requests that graphics related to least squares means be produced via ODS Graphics, provided that
ODS Graphics is enabled and the plot-request does not conflict with other options in the LSMEANS
statement. For general information about ODS Graphics, see Chapter 21, “Statistical Graphics Using
ODS.”
The available options and suboptions are as follows:
ALL
requests that the default plots that correspond to this LSMEANS statement be produced. The
default plot depends on the options in the statement.
ANOMPLOT
ANOM
requests an analysis-of-means display in which least squares means are compared to an average
least squares mean. Least squares mean ANOM plots are produced only for those model effects
that are listed in LSMEANS statements and have options that do not contradict with the display.
For example, the following statements produce analysis-of-mean plots for effects A and C:
lsmeans A / diff=anom plot=anom;
lsmeans B / diff
plot=anom;
lsmeans C /
plot=anom;
The DIFF option in the second LSMEANS statement implies all pairwise differences.
BOXPLOT< boxplot-options >
produces box plots of the distribution of the least squares mean or least squares mean differences across a posterior sample. For example, this plot is available in procedures that support a
Bayesian analysis through the BAYES statement.
A separate box is generated for each estimable function, and all boxes appear on a single graph
by default. You can affect the appearance of the box plot graph with the following options:
ORIENTATION=VERTICAL | HORIZONTAL
ORIENT=VERT | HORIZ
specifies the orientation of the boxes. The default is vertical orientation of the box plots.
NPANELPOS=number
specifies how to break the series of box plots across multiple panels. If the NPANELPOS
option is not specified, or if number equals zero, then all box plots are displayed in a single
graph; this is the default. If a negative number is specified, then exactly up to jnumber j
of box plots are displayed per panel. If number is positive, then the number of boxes per
panel is balanced to achieve small variation in the number of box plots per graph.
464 F Chapter 19: Shared Concepts and Topics
CONTROLPLOT
CONTROL
requests a display in which least squares means are visually compared against a reference level.
These plots are produced only for statements with options that are compatible with control
differences. For example, the following statements produce control plots for effects A and C:
lsmeans A / diff=control('1') plot=control;
lsmeans B / diff
plot=control;
lsmeans C
plot=control;
The DIFF option in the second LSMEANS statement implies all pairwise differences.
DIFFPLOT< (diffplot-options) >
DIFFOGRAM< (diffplot-options) >
DIFF< (diffplot-options) >
requests a display of all pairwise least squares mean differences and their significance. The
display is also known as a “mean-mean scatter plot” when it is based on arithmetic means (Hsu
1996; Hsu and Peruggia 1994). For each comparison a line segment, centered at the LS-means in
the pair, is drawn. The length of the segment corresponds to the projected width of a confidence
interval for the least squares mean difference. Segments that fail to cross the 45-degree reference
line correspond to significant least squares mean differences.
LS-mean difference plots are produced only for statements with options that are compatible with
the display. For example, the following statements request differences against a control level for
the A effect, all pairwise differences for the B effect, and the least squares means for the C effect:
lsmeans A / diff=control('1') plot=diff;
lsmeans B / diff
plot=diff;
lsmeans C
plot=diff;
The DIFF= type in the first statement is incompatible with a display of all pairwise differences.
You can specify the following diffplot-options:
ABS
determines the positioning of the line segments in the plot. This is the default diffplotoptions. When the ABS option is in effect, all line segments are shown on the same side of
the reference line.
NOABS
determines the positioning of the line segments in the plot. The NOABS option separates
comparisons according to the sign of the difference.
CENTER
marks the center point for each comparison. This point corresponds to the intersection of
two least squares means.
NOLINES
suppresses the display of the line segments that represent the confidence bounds for the
differences of the least squares means. The NOLINES option implies the CENTER option.
The default is to draw line segments in the upper portion of the plot area without marking
the center point.
Syntax: LSMEANS Statement F 465
DISTPLOT< distplot-options >
DIST< distplot-options >
generates panels of histograms with a kernel density overlaid if the analysis has access to a set
of posterior parameter estimates. For example, this plot is available in procedures that support
a Bayesian analysis through the BAYES statement. A separate plot in each panel contains the
results for each least squares mean or least squares mean differences. You can specify the
following distplot-options in parentheses:
BOX | NOBOX
controls the display of a horizontal box plot of the estimable function’s distribution across
the posterior sample below the graph. The BOX option is enabled by default.
HIST | NOHIST
controls the display of the histogram of the estimable function’s distribution across the
posterior sample. The HIST option is enabled by default.
NORMAL | NONORMAL
controls the display of a normal density estimate on the graph. The NONORMAL option
is enabled by default.
KERNEL | NOKERNEL
controls the display of a kernel density estimate on the graph. The KERNEL option is
enabled by default.
NROWS=number
specifies the highest number of rows in a panel. The default is 3.
NCOLS=number
specifies the highest number of columns in a panel. The default is 3.
UNPACK
unpacks the panel into separate graphics.
MEANPLOT< (meanplot-options) >
requests displays of the least squares means.
The following meanplot-options control the display of the least squares means.
ASCENDING
displays the least squares means in ascending order. This option has no effect if means are
displayed in separate plots.
CL
displays upper and lower confidence limits for the least squares means. By default, 95%
limits are drawn. You can change the confidence level with the ALPHA= option. Confidence limits are drawn by default if the CL option is specified in the LSMEANS statement.
CLBAND
displays confidence limits as bands. This option implies the JOIN option.
466 F Chapter 19: Shared Concepts and Topics
DESCENDING
displays the least squares means in descending order. This option has no effect if means are
displayed in separate plots.
ILINK
requests that means (and confidence limits) be displayed on the inverse linked scale.
JOIN
CONNECT
connects the least squares means with lines. This option is implied by the CLBAND option. If the effect contains nested variables and a SLICEBY= effect contains classification
variables that appear as crossed effects, this option is ignored.
SLICEBY=fixed-effect
specifies an effect by which to group the means in a single plot. For example, the following
statement requests a plot in which the levels of A are placed on the horizontal axis and the
means that belong to the same level of B are joined by lines:
lsmeans A*B / plot=meanplot(sliceby=b join);
Unless the LS-mean effect contains at least two classification variables, the SLICEBY=
option has no effect. The fixed-effect does not have to be an effect in your MODEL statement, but it must consist entirely of classification variables and it must be contained in the
LS-mean effect.
PLOTBY=fixed-effect
specifies an effect by which to break interaction plots into separate displays. For example,
the following statement requests for each level of C one plot of the A*B cell means that are
associated with that level of C:
lsmeans A*B*C / plot=meanplot(sliceby=b plotby=c clband);
In each plot, levels of A are displayed on the horizontal axis, and confidence bands are
drawn around the means that share the same level of B.
The PLOTBY= option has no effect unless the LS-mean effect contains at least three classification variables. The fixed-effect does not have to be an effect in the MODEL statement,
but it must consist entirely of classification variables and it must be contained in the LSmean effect.
NONE
requests that no plots be produced.
When LS-mean calculations are adjusted for multiplicity by using the ADJUST= option, the plots are
adjusted accordingly.
SEED=number
specifies the seed for the sampling-based components of the computations for the LSMEANS statement (for example, chi-bar-square statistics and simulated p-values). The value of number must be
an integer. The seed is used to start the pseudo-random-number generator for the simulation. If
you do not specify a seed, or if you specify a value less than or equal to zero, the seed is generated
Syntax: LSMEANS Statement F 467
from reading the time of day from the computer clock. Note that there could be multiple LSMEANS
statements with SEED= specifications and there could be other statements that can supply a random
number seed. Since the procedure has only one random number stream, the initial seed is shown in
the SAS log.
SINGULAR=number
tunes the estimability checking. If v is a vector, define ABS(v) to be the largest absolute value of the
elements of v. If ABS(K0 K0 T) is greater than c*number for any row of K0 in the contrast, then
K0 ˇ is declared nonestimable. Here, T is the Hermite form matrix .X0 X/ X0 X, and c is ABS(K0 ),
except when it equals 0, and then c is 1. The value for number must be between 0 and 1; the default
is 1E–4.
STEPDOWN< (step-down-options) >
requests that multiple comparison adjustments for the p-values of LS-mean differences be further adjusted in a step-down fashion. Step-down methods increase the power of multiple comparisons by taking advantage of the fact that a p-value is never declared significant unless all smaller p-values are also
declared significant. The STEPDOWN adjustment combined with ADJUST=BON corresponds to the
methods of Holm (1979) “Method 2” of Shaffer (1986); this is the default. Using step-down-adjusted
p-values combined with ADJUST=SIMULATE corresponds to the method of Westfall (1997).
If the denominator degrees of freedom are computed by the Kenward-Roger (Kenward and Roger
1997) or Satterthwaite method in a mixed model, then step-down-adjusted p-values are produced
only if the ADJDFE=ROW option is in effect.
Also, STEPDOWN affects only p-values, not confidence limits. For ADJUST=SIMULATE, the generalized least squares hybrid approach of Westfall (1997) is used to increase Monte Carlo accuracy.
You can specify the following step-down-options in parentheses:
MAXTIME=n
specifies the time (in seconds) to be spent computing the maximal logically consistent sequential subsets of equality hypotheses for TYPE=LOGICAL. The default is MAXTIME=60. If the
MAXTIME value is exceeded, the adjusted tests are not computed. When this occurs, you can
try increasing the MAXTIME value. However, note that there are common multiple comparisons problems for which this computation requires a huge amount of time—for example, all
pairwise comparisons between more than 10 groups. In such cases, try to use TYPE=FREE (the
default) or TYPE=LOGICAL(n) for small n.
REPORT
specifies that a report on the step-down adjustment be displayed, including a listing of the sequential subsets (Westfall 1997) and, for ADJUST=SIMULATE, the step-down simulation results.
TYPE=LOGICAL< (n) >
TYPE=FREE
specifies how step-down adjustment are made. If you specify TYPE=LOGICAL, the step-down
adjustments are computed by using maximal logically consistent sequential subsets of equality
hypotheses (Shaffer 1986; Westfall 1997). Alternatively, for TYPE=FREE, sequential subsets
are computed ignoring logical constraints. The TYPE=FREE results are more conservative
than those for TYPE=LOGICAL, but they can be much more efficient to produce for many
468 F Chapter 19: Shared Concepts and Topics
comparisons. For example, it is not feasible to take logical constraints between all pairwise
comparisons of more than 10 groups. For this reason, TYPE=FREE is the default.
However, you can reduce the computational complexity of taking logical constraints into account by limiting the depth of the search tree used to compute them, specifying the optional
depth parameter as a number n in parentheses after TYPE=LOGICAL. As with TYPE=FREE,
results for TYPE=LOGICAL(n) are conservative relative to the true TYPE=LOGICAL results.
But even for TYPE=LOGICAL(0) they can be appreciably less conservative than TYPE=FREE,
and they are computationally feasible for much larger numbers of comparisons. If you do not
specify n or if n = –1, the full search tree is used.
ODS Table Names: LSMEANS Statement
Each table created by the LSMEANS statement has a name associated with it, and you can use this name
to refer to the table when using the Output Delivery System (ODS) to select tables and create output data
sets. These names are listed in Table 19.22. For more information about ODS, see Chapter 20, “Using the
Output Delivery System.”
Table 19.22
ODS Tables Produced by the LSMEANS statement
Table Name
Description
Required Option
Coef
Diffs
L matrix coefficients
Differences of LS-means
LSMeans
LSMLines
LS-means
Lines display for LS-means
E
DIFF or ADJUST= or
STEPDOWN
Default
LINES
ODS Graphics: LSMEANS Statement
This section describes the use of ODS Graphics for creating graphics that are related to LS-means in procedures that support the common LSMEANS or SLICE statement. There are two groups of available plots:
those that can be produced by all procedures that support these two statements, and those that can be produced only in association with the three procedures that can perform Bayesian analysis (PROC GENMOD,
PROC LIFEREG, and PROC PHREG). Plots that are associated with the Bayesian analysis are available
via these procedures directly, and also by using PROC PLM with an item store that was created by these
procedures.
Plots in the first group depict the LS-means and their differences; when LS-mean comparisons are adjusted
for multiplicity by using the ADJUST= option, the plots are adjusted accordingly. To request plots in this
group, ODS Graphics must be enabled and you must request plots with the appropriate PLOTS= option in
the LSMEANS or SLICE statement. Plots in the second group depict the posterior sample distribution of
LS-means and their differences. To request plots in this group, you must also use a BAYES statement with
PROC GENMOD, PROC PHREG, or PROC LIFEREG, or you must use PROC PLM to perform statistical
analysis on an item store that was saved from a Bayesian analysis.
ODS Graphics: LSMEANS Statement F 469
For more information about ODS Graphics, see Chapter 21, “Statistical Graphics Using ODS.” The available
graphs are summarized in Table 19.23 and Table 19.24.
Table 19.23 Graphs Produced by All Procedures That Support the Common LSMEANS or SLICE Statement
ODS Graph Name
Plot Description
Required Option
AnomPlot
Requests an analysis of means display in which least squares means are
compared to an average least squares
mean.
Requests a display in which least
squares means are compared to a reference level.
Displays all pairwise least squares
mean differences and their significance. This plot is also known as a
“mean-mean scatter plot” when based
on arithmetic means.
Displays least squares means.
PLOTS=ANOM
ControlPlot
DiffPlot
MeanPlot
Table 19.24
PLOTS=CONTROL
PLOTS=DIFF
PLOTS=MEANPLOT
Graphs Produced by Procedures That Support the LSMEANS or SLICE Statement and
Bayesian Analysis
ODS Graph Name
Plot Description
Required Option
BoxPlot
Displays box plots of LS-means or
LS-mean differences across a posterior sample.
Displays panels of histograms with
kernel density curves overlaid. Each
plot contains the results for the posterior sample of each LS-mean or LSmean difference.
Displays a histogram with a kernel
density curve overlaid. The plot contains the results for the posterior sample of the LS-mean or LS-mean difference.
PLOTS=BOXPLOT
DistPanel
DistPlot
PLOTS=DISTPLOT
PLOTS=DISTPLOT(UNPACK)
You can supply the same plot-options to the SLICE statement to produce these graphs. For details about
the plot-options of the LSMEANS or SLICE statement, see the PLOTS= option in the section “LSMEANS
Statement” on page 453. For more details about the DIFFPLOT in particular, see the section “Graphics for
LS-Mean Comparisons” on page 3122 in Chapter 41, “The GLIMMIX Procedure.”
470 F Chapter 19: Shared Concepts and Topics
LSMESTIMATE Statement
This statement documentation applies to the following SAS/STAT procedures:
GENMOD, LIFEREG, LOGISTIC, MIXED, ORTHOREG, PHREG, PLM, PROBIT, SURVEYLOGISTIC,
SURVEYPHREG, and SURVEYREG. It also applies to the RELIABILITY procedure in SAS/QC software.
The LSMESTIMATE statement in the GLIMMIX procedure is documented in Chapter 41, “The GLIMMIX
Procedure.”
The LSMESTIMATE statement provides a mechanism for obtaining custom hypothesis tests among least
squares means. In contrast to the LSMEANS statement, the LSMESTIMATE statement does not produce
the least squares means or their differences; instead, you can estimate any linear function of the least squares
means (including the means themselves or their differences). In contrast to the linear functions that are
constructed with the ESTIMATE statement, you do not specify coefficients for the individual parameter
estimates. Instead, with the LSMESTIMATE statement you specify coefficients for the least squares means;
these are then converted for you into estimable functions for the parameter estimates.
The LSMESTIMATE statement thus combines important and convenient features of the LSMEANS and the
ESTIMATE statement. As with the LSMEANS statement, the following conditions are true:
You need to specify only a single effect; the mapping into linear estimable functions in terms of the
parameter estimates is performed by the procedure.
You can use the AT=, BYLEVEL, and OBSMARGINS options to affect the computation of the underlying least squares means.
As with the ESTIMATE statement you can do the following:
specify multiple-row linear combinations.
perform multiplicity corrections to control the familywise Type I error probability with the ADJUST=
option.
construct general linear functions of the least squares means.
perform joint F or chi-square tests with or without order restrictions through the JOINT option.
rely on positional or nonpositional syntax to specify coefficients for linear functions. For details about
using nonpositional syntax, see the section “Positional and Nonpositional Syntax for Coefficients in
Linear Functions” on page 448.
The computation of an LSMESTIMATE involves two coefficient matrices. Suppose that there are nl levels
for a valid least squares means effect (an effect that is part of your model and consists of classification
variables only). Then the LS-means are formed as L1b̌, where L1 is a .nl p/ coefficient matrix. The
.k nl / coefficient matrix K is formed from the values that you supply in the k rows of the LSMESTIMATE
statement. The least squares means estimates then represent the .k 1/ vector
KL1 ˇ D Lˇ
Syntax: LSMESTIMATE Statement F 471
Because the analytic features and capabilities of the LSMESTIMATE statement are an amalgam of the
LSMEANS and the ESTIMATE statement, the syntax of the statement follows the same pattern.
Syntax: LSMESTIMATE Statement
LSMESTIMATE model-effect < ‘label’ > values < divisor =n >
< , < ‘label’ > values < divisor =n > > < , . . . >
< / options > ;
In contrast to a multirow estimate in the ESTIMATE statement, you specify only a single effect in the
LSMESTIMATE statement. The row labels are optional and follow the model-effect specification. For
example, the following statements fit a split-split-plot design and compare the average of the third and
fourth LS-mean of the whole-plot factor A to the first LS-mean of the factor:
proc glimmix;
class a b block;
model y = a b a*b / s;
random int a / sub=block;
lsmestimate A 'a1 vs avg(a3,a4)' 2 0 -1 -1 divisor=2;
run;
The order in which coefficients are assigned to the least squares means corresponds to the order in which
they are displayed in the “Least Squares Means” table. You can use the ELSM option to see how coefficients
are matched to levels of the fixed effect.
The optional divisor=n specification enables you to assign a separate divisor to each row of the LSMESTIMATE. You can also assign divisor values through the DIVISOR= option. See the description of the
DIVISOR= option that follows for the interaction between the two ways of specifying divisors.
Table 19.25 summarizes important options in the LSMESTIMATE statement. All LSMESTIMATE options
are subsequently discussed in alphabetical order.
Table 19.25 LSMESTIMATE Statement Options
Option
Description
Construction and Computation of LS-Means
AT
Modifies covariate values in computing LS-means
BYLEVEL
Computes separate margins
DIVISOR=
Specifies a list of values to divide the coefficients
OM=
Specifies the weighting scheme for LS-means computation as determined by a data set
SINGULAR=
Tunes estimability checking
472 F Chapter 19: Shared Concepts and Topics
Table 19.25 continued
Option
Description
Degrees of Freedom and p-values
ADJUST=
Determines the method for multiple-comparison adjustment of LSmeans differences
ALPHA=˛
Determines the confidence level (1 ˛)
LOWER
Performs one-sided, lower-tailed inference
STEPDOWN
Adjusts multiple-comparison p-values further in a step-down fashion
TESTVALUE=
Specifies values under the null hypothesis for tests
UPPER
Performs one-sided, upper-tailed inference
Statistical Output
CL
CORR
COV
E
ELSM
JOINT
PLOTS=
SEED=
Constructs confidence limits for means and mean differences
Displays the correlation matrix of LS-means
Displays the covariance matrix of LS-means
Prints the L matrix
Prints the K matrix
Produces a joint F or chi-square test for the LS-means and LSmeans differences
Requests graphs of means and mean comparisons
Specifies the seed for computations that depend on random
numbers
Generalized Linear Modeling
CATEGORY=
Specifies how to construct estimable functions with multinomial
data
EXP
Exponentiates and displays LS-means estimates
ILINK
Computes and displays estimates and standard errors of LS-means
(but not differences) on the inverse linked scale
You can specify the following options in the LSMESTIMATE statement after a slash (/):
ADJDFE=SOURCE
ADJDFE=ROW
specifies how denominator degrees of freedom are determined when p-values and confidence limits
are adjusted for multiple comparisons with the ADJUST= option. When you do not specify the
ADJDFE= option or when you specify ADJDFE=SOURCE, the denominator degrees of freedom for
multiplicity-adjusted results are the denominator degrees of freedom for the LS-mean effect in the
“Type III Tests of Fixed Effects” table.
The ADJDFE=ROW setting is useful if you want multiplicity adjustments to take into account that
denominator degrees of freedom are not constant across estimates. For example, this can be the
case when the denominator degrees of freedom are computed by the Satterthwaite or Kenward-Roger
method (Kenward and Roger 1997) in a mixed model.
Syntax: LSMESTIMATE Statement F 473
The ADJDFE= option is not supported by the procedures that perform chi-square-based inference
(GENMOD, LOGISTIC, PHREG and SURVEYLOGISTIC).
ADJUST=BON
ADJUST=SCHEFFE
ADJUST=SIDAK
ADJUST=SIMULATE< (simoptions) >
ADJUST=T
requests a multiple comparison adjustment for the p-values and confidence limits for the LS-mean
estimates. The adjusted quantities are produced in addition to the unadjusted p-values and confidence limits. Adjusted confidence limits are produced if the CL or ALPHA= option is in effect.
For a description of the adjustments, see Chapter 42, “The GLM Procedure,” and Chapter 61, “The
MULTTEST Procedure,” in addition to the documentation for the ADJUST= option in the LSMEANS
statement.
Not all adjustment methods of the LSMEANS statement are available for the LSMESTIMATE statement. Multiplicity adjustments in the LSMEANS statement are designed specifically for differences
of least squares means.
If you specify the STEPDOWN option, the p-values are further adjusted in a step-down fashion.
ALPHA=number
requests that a t type confidence interval be constructed for each of the LS-means with confidence
level 1 – number. The value of number must be between 0 and 1; the default is 0.05.
AT variable=value
AT (variable-list)=(value-list)
AT MEANS
modifies the values of the covariates used in computing LS-means. See the AT option in the
LSMEANS statement for details.
BYLEVEL
requests that the procedure compute separate margins for each level of the LSMEANS effect.
The standard LS-means have equal coefficients across classification effects. The BYLEVEL option
changes these coefficients to be proportional to the observed margins. This adjustment is reasonable
when you want your inferences to apply to a population that is not necessarily balanced but has the
margins observed in the input data set. In this case, the resulting LS-means are actually equal to
raw means for fixed-effects models and certain balanced random-effects models, but their estimated
standard errors account for the covariance structure that you have specified. If a WEIGHT statement
is specified, the procedure uses weighted margins to construct the LS-means coefficients.
If the AT option is specified, the BYLEVEL option disables it.
CATEGORY=category-options
specifies how to construct estimates and multiplicity corrections for models with multinomial data
(ordinal or nominal). This option is also important for constructing sets of estimable functions for F
tests with the JOINT option.
The category-options indicate how response variable levels are treated in constructing the estimable
functions. Possible value for the category-options are the following:
474 F Chapter 19: Shared Concepts and Topics
JOINT
computes the estimable functions for every nonredundant category and treats them as a set. For
example, a three-row LSMESTIMATE statement in a model with three response categories leads
to six estimable functions.
SEPARATE
computes the estimable functions for every nonredundant category in turn. For example, a threerow LSMESTIMATE statement in a model with three response categories leads to two sets of
three estimable functions.
quoted-value-list
computes the estimable functions only for the list of values given. The list must consist of
formatted values of the response categories.
For further details about using the CATEGORY= option in models for multinomial data, see the
documentation for the CATEGORY= option in the ESTIMATE statement.
The CATEGORY= option is supported only by the procedures that support generalized linear modeling (GENMOD, LOGISTIC, and SURVEYLOGISTIC) and by PROC PLM when it is used to perform
statistical analyses on item stores that were created by these procedures.
CHISQ
requests that chi-square tests be performed in addition to F tests, when you request an F test with the
JOINT option. This option has no effect in procedures that produce chi-square statistics by default.
CL
requests that t type confidence limits be constructed for each of the LS-means. The confidence level
is 0.95 by default; this can be changed with the ALPHA= option. If you specify an ADJUST= option,
then the confidence limits are adjusted for multiplicity. But if you also specify STEPDOWN, then
only p-values are step-down adjusted, not the confidence limits.
CORR
displays the estimated correlation matrix of the linear combination of the least squares means.
COV
displays the estimated covariance matrix of the linear combination of the least squares means.
DF=number
specifies the degrees of freedom for the tests and confidence limits. The option is not supported
by the procedures that perform chi-square-based inference (GENMOD, LOGISTIC, PHREG, and
SURVEYLOGISTIC).
DIVISOR=value-list
specifies a list of values by which to divide the coefficients so that fractional coefficients can be
entered as integer numerators. If you do not specify value-list, a default value of 1.0 is assumed.
Missing values in the value-list are converted to 1.0.
If the number of elements in value-list exceeds the number of rows of the estimate, the extra values
are ignored. If the number of elements in value-list is less than the number of rows of the estimate,
the last value in value-list is carried forward.
If you specify a row-specific divisor as part of the specification of the estimate row, this value multiplies the corresponding value in the value-list. For example, the following statement divides the
coefficients in the first row by 8, and the coefficients in the third and fourth row by 3:
Syntax: LSMESTIMATE Statement F 475
lsmestimate A 'One
'One
'One
'One
vs.
vs.
vs.
vs.
two'
three'
four'
five'
8 -8
divisor=2,
1 0 -1
,
3 0 0 -3
,
3 0 0 0 -3 / divisor=4,.,3;
Coefficients in the second row are not altered.
E
requests that the L coefficients of the estimable function be displayed. These are the coefficients that
apply to the fixed-effect parameter estimates. The E option displays the coefficients that you would
need to enter in an equivalent ESTIMATE statement.
ELSM
requests that the K matrix coefficients be displayed. These are the coefficients that apply to the LSmeans. This option is useful to ensure that you assigned the coefficients correctly to the LS-means.
EXP
requests exponentiation of the least squares means estimate. When you model data with the logit
link function and the estimate represents a log odds ratio, the EXP option produces an odds ratio.
If you specify the CL or ALPHA= option, the (adjusted) confidence limits for the estimate are also
exponentiated.
The EXP option is supported only by PROC PHREG, PROC SURVEYPHREG, the procedures
that support generalized linear modeling (GENMOD, LOGISTIC, and SURVEYLOGISTIC), and
by PROC PLM when it is used to perform statistical analyses on item stores that were created by
these procedures.
ILINK
requests that the estimate and its standard error also be reported on the scale of the mean (the inverse
linked scale). The computation of the inverse linked estimate depends on the estimation mode. For
example, if the analysis is based on a posterior sample when a BAYES statement is present, the
inversely linked estimate is the average of the inversely linked values across the sample of posterior
parameter estimates. If the analysis is not based on a sample of parameter estimates, the procedure
computes the value on the mean scale by applying the inverse link to the estimate.
The interpretation of the inversely linked quantity depends on the coefficients that are specified in
your LSMESTIMATE statement and the link function. For example, in a model for binary data with
logit link the following LSMESTIMATE statement computes
qD
1
1 C expf .1
2 /g
where 1 and 2 are the least squares means that are associated with the first two levels of the classification effect A:
proc logistic;
class A / param=glm;
model y = A / dist=binary link=logit;
lsmestimate A 1 -1 / ilink;
run;
476 F Chapter 19: Shared Concepts and Topics
The quantity q is not the difference of the probabilities associated with the two levels,
1
2 D
1
1 C expf 1 g
1
1 C expf 2 g
The standard error of the inversely linked estimate is based on the delta method. If you also specify
the CL or ALPHA= option, the procedure computes confidence intervals for the inversely linked
estimate. These intervals are obtained by applying the inverse link to the confidence intervals on the
linked scale.
The ILINK option is supported only by the procedures that support generalized linear modeling
(GENMOD, LOGISTIC, and SURVEYLOGISTIC) and by PROC PLM when it is used to perform
statistical analyses on item stores that were created by these procedures.
JOINT< (joint-test-options) >
requests that a joint F or chi-square test be produced for the rows of the estimate. For more information about the simulation-based p-value calculation, see the section “Joint Hypothesis Tests with
Complex Alternatives, the Chi-Bar-Square Statistic” on page 451. You can specify the following
joint-test-options in parentheses:
ACC=
specifies the accuracy radius for determining the necessary sample size in the simulation-based
approach of Silvapulle and Sen (2004) for tests with order restrictions. The value of must be
strictly between 0 and 1; the default value is 0.005.
EPS=
specifies the accuracy confidence level for determining the necessary sample size in the
simulation-based approach of Silvapulle and Sen (2004) for F tests with order restrictions. The
value of must be strictly between 0 and 1; the default value is 0.01.
LABEL=‘label’
assigns an identifying label to the joint test. If you do not specify a label, the first non-default
label for the ESTIMATE rows is used to label the joint test.
NOEST
ONLY
performs only the joint test and suppresses other results from the ESTIMATE statement. This
option is useful for emulating the CONTRAST statement that is available in other procedures.
NSAMP=n
specifies the number of samples for the simulation-based method of Silvapulle and Sen (2004).
If n is not specified, it is constructed from the values of the ALPHA=˛, the ACC=, and the
EPS= options. With the default values for , , and ˛ (0.005, 0.01, and 0.05, respectively),
NSAMP=12,604 by default.
CHISQ
adds a chi-square test if the procedure produces an F test by default.
BOUNDS=value-list
specifies boundary values for the estimable linear function. The null value of the hypothesis
is always zero. If you specify a positive boundary value z, the hypotheses are H W D 0,
Syntax: LSMESTIMATE Statement F 477
Ha W W > 0 with the added constraint that < z. The same is true for negative boundary
values. The alternative hypothesis is then Ha W < 0 subject to the constraint > jzj. If
you specify a missing value, the hypothesis is assumed to be two-sided. The BOUNDS option
enables you to specify sets of one- and two-sided joint hypotheses. If all values in value-list are
set to missing, the procedure performs a simulation-based p-value calculation for a two-sided
test.
LOWER
LOWERTAILED
requests that the p-value for the t test be based only on values that are less than the test statistic. A
two-tailed test is the default. A lower-tailed confidence limit is also produced if you specify the CL
or ALPHA= option.
Note that for ADJUST=SCHEFFE the one-sided adjusted confidence intervals and one-sided adjusted
p-values are the same as the corresponding two-sided statistics, because this adjustment is based on
only the right tail of the F distribution.
If you request an F test with the JOINT option, then a one-sided left-tailed order restriction is applied
to all estimable functions, and the corresponding chi-bar-square statistic of Silvapulle and Sen (2004)
is computed in addition to the two-sided, standard, F or chi-square statistic. See the JOINT option for
how to control the computation of the simulation-based chi-bar-square statistic.
OBSMARGINS< =OM-data-set >
OM< =OM-data-set >
specifies a potentially different weighting scheme for the computation of LS-means coefficients. The
standard LS-means have equal coefficients across classification effects; however, the OM option
changes these coefficients to be proportional to those found in the OM-data-set. This adjustment
is reasonable when you want your inferences to apply to a population that is not necessarily balanced
but has the margins observed in OM-data-set. See the OBSMARGINS option in the LSMEANS
statement for further details.
PLOTS=plot-options
produces ODS statistical graphics of the distribution of estimable functions if the procedure performs
the analysis in a sampling-based mode. For example, this is the case when procedures support a
BAYES statement and perform a Bayesian analysis. The estimable functions are then computed for
each of the posterior parameter estimates, and the “Least Squares Means Estimates” table reports
simple descriptive statistics for the evaluated functions. In this situation, the PLOTS= option enables
you to visualize the distribution of the estimable function. The following plot-options are available:
ALL
produces all possible plots with their default settings.
BOXPLOT< (boxplot-options) >
produces box plots of the distribution of the estimable function across the posterior sample. A
separate box plot is generated for each estimable function and all box plots appear on a single
graph by default. You can affect the appearance of the box plot graph with the following options:
478 F Chapter 19: Shared Concepts and Topics
ORIENTATION=VERTICAL | HORIZONTAL
ORIENT=VERT | HORIZ
specifies the orientation of the boxes. The default is vertical orientation of the box plots.
NPANELPOS=number
specifies how to break the series of box plots across multiple panels. If the NPANELPOS
option is not specified, or if number equals zero, then all box plots are displayed in a single
graph; this is the default. If a negative number is specified, then exactly up to jnumber j
of box plots are displayed per panel. If number is positive, then the number of boxes per
panel is balanced to achieve small variation in the number of box plots per graph.
DISTPLOT< (distplot-options) >
DIST< (distplot-options) >
generates panels of histograms with a kernel density overlaid. A separate plot in each panel
contains the results for each estimable function. You can specify the following distplot-options
in parentheses:
BOX | NOBOX
controls the display of a horizontal box plot below the histogram. The BOX option is
enabled by default.
HIST | NOHIST
controls the display of the histogram of the estimable function’s distribution across the
posterior sample. The HIST option is enabled by default.
NORMAL | NONORMAL
controls the display of a normal density estimate on the graph. The NONORMAL option
is enabled by default.
KERNEL | NOKERNEL
controls the display of a kernel density estimate on the graph. The KERNEL option is
enabled by default.
NROWS=number
specifies the highest number of rows in a panel. The default is 3.
NCOLS=number
specifies the highest number of columns in a panel. The default is 3.
UNPACK
unpacks the panel into separate graphics.
NONE
does not produce any plots.
SEED=number
specifies the seed for the sampling-based components of the computations for the LSMESTIMATE
statement (for example, chi-bar-square statistics and simulated p-values). The value of number must
be an integer. The seed is used to start the pseudo-random-number generator for the simulation. If you
do not specify a seed, or if you specify a value less than or equal to zero, the seed is generated from
Syntax: LSMESTIMATE Statement F 479
reading the time of day from the computer clock. Note that there could be multiple LSMESTIMATE
statements with SEED= specifications and there could be other statements that can supply a random
number seed. Since the procedure has only one random number stream, the initial seed is shown in
the SAS log.
SINGULAR=number
tunes the estimability checking as documented for the SINGULAR= option in the ESTIMATE statement.
STEPDOWN< (step-down-options) >
requests that multiplicity adjustments for the p-values of estimable functions be further adjusted in a
step-down fashion. Step-down methods increase the power of multiple testing procedures by taking
advantage of the fact that a p-value is never declared significant unless all smaller p-values are also
declared significant. The STEPDOWN adjustment combined with ADJUST=BON corresponds to
the methods of Holm (1979) and “Method 2” of Shaffer (1986); this is the default. Using stepdown-adjusted p-values combined with ADJUST=SIMULATE corresponds to the method of Westfall
(1997).
If the ESTIMATE statement is applied with a STEPDOWN option in a mixed model where the
degrees-of-freedom method is that of Kenward and Roger (1997) or of Satterthwaite, then step-downadjusted p-values are produced only if the ADJDFE=ROW option is in effect.
Also, the STEPDOWN option affects only p-values, not confidence limits. For ADJUST=SIMULATE,
the generalized least squares hybrid approach of Westfall (1997) is used to increase Monte Carlo
accuracy.
You can specify the following step-down-options in parentheses:
MAXTIME=n
specifies the time (in seconds) to be spent computing the maximal logically consistent sequential subsets of equality hypotheses for TYPE=LOGICAL. The default is MAXTIME=60. If the
MAXTIME value is exceeded, the adjusted tests are not computed. When this occurs, you can
try increasing the MAXTIME value. However, note that there are common multiple comparisons problems for which this computation requires a huge amount of time—for example, all
pairwise comparisons between more than 10 groups. In such cases, try to use TYPE=FREE (the
default) or TYPE=LOGICAL(n) for small n.
ORDER=PVALUE
ORDER=ROWS
specifies the order in which the step-down tests are performed. ORDER=PVALUE is the default,
with LS-mean estimates being declared significant only if all LS-mean estimates with smaller
(unadjusted) p-values are significant. If you specify ORDER=ROWS, then significances are
evaluated in the order in which they are specified.
REPORT
specifies that a report on the step-down adjustment be displayed, including a listing of the sequential subsets (Westfall 1997) and, for ADJUST=SIMULATE, the step-down simulation results.
480 F Chapter 19: Shared Concepts and Topics
TYPE=LOGICAL< (n) >
TYPE=FREE
specifies how step-down adjustment are made. If you specify TYPE=LOGICAL, the step-down
adjustments are computed by using maximal logically consistent sequential subsets of equality
hypotheses (Shaffer 1986; Westfall 1997). Alternatively, for TYPE=FREE, sequential subsets
are computed ignoring logical constraints. The TYPE=FREE results are more conservative than
those for TYPE=LOGICAL, but they can be much more efficient to produce for many estimates.
For example, it is not feasible to take logical constraints between all pairwise comparisons of
more than about 10 groups. For this reason, TYPE=FREE is the default.
However, you can reduce the computational complexity of taking logical constraints into account by limiting the depth of the search tree used to compute them, specifying the optional
depth parameter as a number n in parentheses after TYPE=LOGICAL. As with TYPE=FREE,
results for TYPE=LOGICAL(n) are conservative relative to the true TYPE=LOGICAL results.
But even for TYPE=LOGICAL(0), they can be appreciably less conservative than TYPE=FREE,
and they are computationally feasible for much larger numbers of estimates. If you do not specify n or if n = –1, the full search tree is used.
TESTVALUE=value-list
TESTMEAN=value-list
specifies the value under the null hypothesis for testing the estimable functions in the LSMESTIMATE
statement. The rules for specifying the value-list are very similar to those for specifying the divisor
list in the DIVISOR= option. If no TESTVALUE= is specified, all tests are performed as H W Lˇ D 0.
Missing values in the value-list also are translated to zeros. If you specify fewer values than rows in
the LSMESTIMATE statement, the last value in value-list is carried forward.
The TESTVALUE= option affects only p-values from individual, joint, and multiplicity-adjusted tests.
It does not affect confidence intervals.
The TESTVALUE option is not available for the multinomial distribution, and the values are ignored
when you perform a sampling-based (Bayesian) analysis.
UPPER
UPPERTAILED
requests that the p-value for the t test be based only on values that are greater than the test statistic. A
two-tailed test is the default. An upper-tailed confidence limit is also produced if you specify the CL
or ALPHA= option.
Note that for ADJUST=SCHEFFE the one-sided adjusted confidence intervals and one-sided adjusted
p-values are the same as the corresponding two-sided statistics, because this adjustment is based on
only the right tail of the F distribution.
If you request a joint test with the JOINT option, then a one-sided right-tailed order restriction is
applied to all estimable functions, and the corresponding chi-bar-square statistic of Silvapulle and
Sen (2004) is computed in addition to the two-sided, standard, F or chi-square statistic. See the
JOINT option for how to control the computation of the simulation-based chi-bar-square statistic.
ODS Graphics: LSMESTIMATE Statement F 481
ODS Table Names: LSMESTIMATE Statement
Each table created by the LSMESTIMATE statement has a name associated with it, and you can use this
name to refer to the table when using the Output Delivery System (ODS) to select tables and create output
data sets. These names are listed in Table 19.26. For more information about ODS, see Chapter 20, “Using
the Output Delivery System.”
Table 19.26
ODS Tables Produced by the LSMESTIMATE statement
Table Name
Description
Required Option
Coef
L matrix coefficients or K matrix coefficients
Estimates among LS-means
Joint test results for LS-means estimates
E or ELSM
LSMEstimates
Contrasts
Default
JOINT
ODS Graphics: LSMESTIMATE Statement
This section describes the use of ODS for creating statistical graphs of the distribution of LS-means and LSmean differences with the LSMESTIMATE statement. The plots can be produced only in association with
the three procedures that can perform Bayesian analysis (PROC GENMOD, PROC LIFEREG, and PROC
PHREG). The plots are available via these procedures directly, and also via PROC PLM when run using an
item store that was created by these procedures. To request these graphs, you must do the following:
ensure that ODS Graphics is enabled
use a BAYES statement with PROC GENMOD, PROC LIFEREG, or PROC PHREG, or use PROC
PLM to perform statistical analysis on an item store that was saved from a Bayesian analysis
request plots with the PLOTS= option in the LSMESTIMATE statement
For more information about ODS Graphics, see Chapter 21, “Statistical Graphics Using ODS.” The available
graphs are summarized in Table 19.27.
Table 19.27
Graphs Produced by the LSMESTIMATE statement
ODS Graph Name
Plot Description
Required Option
BoxPlot
Displays box plots of LS-means or
LS-mean differences across a posterior sample.
Displays panels of histograms with
kernel density curves overlaid. Each
plot contains the results for the posterior sample of each LS-mean or LSmean difference.
PLOTS=BOXPLOT
DistPanel
PLOTS=DISTPLOT
482 F Chapter 19: Shared Concepts and Topics
Table 19.27 continued
ODS Graph Name
Plot Description
Required Option
DistPlot
Displays a histogram with a kernel
density curve overlaid. The plot contains the results for the posterior sample of the LS-mean or LS-mean difference.
PLOTS=DISTPLOT(UNPACK)
For details about the plot-options of the LSMESTIMATE statement, see the PLOTS= option in the section
“LSMESTIMATE Statement” on page 470.
NLOPTIONS Statement
This section applies to the following procedures:
CALIS, GLIMMIX, HPMIXED, PHREG, SURVEYPHREG, and VARIOGRAM. See the individual procedure chapters for deviations from the common syntax and defaults shown here.
Syntax: NLOPTIONS Statement
The NLOPTIONS statement provides you with syntax to control aspects of the nonlinear optimizations in
the CALIS, GLIMMIX, HPMIXED, PHREG, SURVEYPHREG, and VARIOGRAM procedures.
NLOPTIONS < options > ;
The nonlinear optimization options are described in alphabetical order after Table 19.28, which summarizes
the options by category. The notation used in describing the options is generic in the sense that denotes
the p 1 vector of parameters for the optimization and i is its ith element. The objective function being
minimized, its p 1 gradient vector, and its p p Hessian matrix are denoted as f . /, g. /, and H. /,
respectively. The gradient with respect to the ith parameter is denoted as gi . /. Superscripts in parentheses
denote the iteration count; for example, f . /.k/ is the value of the objective function at iteration k. In the
mixed model procedures, the parameter vector might consist of fixed effects only, covariance parameters
only, or fixed effects and covariance parameters. In the CALIS procedure, consists of all independent
parameters that are defined in the models and in the PARAMETERS statement.
Table 19.28 Options to Control Aspects of the Optimization
Option
Description
Optimization
HESCAL=
INHESSIAN=
LINESEARCH=
LSPRECISION=
RESTART=
TECHNIQUE=
Determines the type of Hessian scaling
Specifies the start for approximated Hessian
Specifies the line-search method
Specifies the line-search precision
Specifies the iteration number for update restart
Determines the minimization technique
Syntax: NLOPTIONS Statement F 483
Table 19.28 continued
Option
Description
UPDATE=
Determines the update technique
Termination Criteria
ABSCONV=
ABSFCONV=
ABSGCONV=
ABSXCONV=
FCONV=
FCONV2=
FSIZE=
GCONV=
GCONV2=
MAXFUNC=
MAXITER=
MAXTIME=
MINITER=
XCONV=
XSIZE=
Tunes an absolute function convergence criterion
Tunes an absolute function difference convergence criterion
Tunes the absolute gradient convergence criterion
Tunes the absolute parameter convergence criterion
Tunes the relative function convergence criterion
Tunes another relative function convergence criterion
Specifies the value used in the FCONV and GCONV criteria
Tunes the relative gradient convergence criterion
Tunes another relative gradient convergence criterion
Specifies the maximum number of function calls
Specifies the maximum number of iterations
Specifies the upper limit for seconds of CPU time
Specifies the minimum number of iterations
Specifies the relative parameter convergence criterion
Specifies the value used in the XCONV criterion
Step Length
DAMPSTEP=
INSTEP=
MAXSTEP=
Dampens steps in a line search
Specifies the initial trust region radius
Specifies the maximum trust region radius
Printed Output
PALL
PHISTORY
NOPRINT
Displays (almost) all printed output
Displays optimization history
Suppresses all printed output
Covariance Matrix Tolerances
ASINGULAR=
Specifies the absolute singularity for inertia
MSINGULAR=
Specifies the relative M singularity for inertia
VSINGULAR=
Specifies the relative V singularity for inertia
Constraint Specifications
LCEPSILON=
Specifies the range for active constraints
LCDEACT=
Specifies the LM tolerance for deactivating
LCSINGULAR=
Specifies the tolerance for dependent constraints
Remote Monitoring
SOCKET=
Specifies the fileref for remote monitoring
484 F Chapter 19: Shared Concepts and Topics
ABSCONV=r
ABSTOL=r
specifies an absolute function convergence criterion: for minimization, termination requires
f . .k/ / r. The default value of r is the negative square root of the largest double-precision
value, which serves only as a protection against overflows.
ABSFCONV=r < n >
ABSFTOL=r < n >
specifies an absolute function difference convergence criterion:
For all techniques except NMSIMP (specified by the TECHNIQUE= option), termination requires a small change of the function value in successive iterations,
.k 1/
jf .
/
f.
.k/
/j r
The same formula is used for the NMSIMP technique, but .k/ is defined as the vertex with the
lowest function value, and .k 1/ is defined as the vertex with the highest function value in the
simplex.
The default value is r = 0. The optional integer value n specifies the number of successive iterations
for which the criterion must be satisfied before the process can be terminated.
ABSGCONV=r < n >
ABSGTOL=r < n >
specifies an absolute gradient convergence criterion:
For all techniques except NMSIMP (specified by the TECHNIQUE= option), termination requires the maximum absolute gradient element to be small:
max jgj .
j
.k/
/j r
This criterion is not used by the NMSIMP technique.
The default value is r = 1E–5. The optional integer value n specifies the number of successive iterations for which the criterion must be satisfied before the process can be terminated.
ABSXCONV=r < n >
ABSXTOL=r < n >
specifies an absolute parameter convergence criterion:
For all techniques except NMSIMP, termination requires a small Euclidean distance between
successive parameter vectors,
k
.k/
.k 1/
k2 r
For the NMSIMP technique, termination requires either a small length ˛ .k/ of the vertices of a
restart simplex,
˛ .k/ r
Syntax: NLOPTIONS Statement F 485
or a small simplex size,
ı .k/ r
where the simplex size ı .k/ is defined as the L1 distance from the simplex vertex .k/ with the
.k/
smallest function value to the other p simplex points l ¤ .k/ :
ı .k/ D
X
k
.k/
l
.k/ k1
l ¤y
The default is r = 1E–8 for the NMSIMP technique and r = 0 otherwise. The optional integer value
n specifies the number of successive iterations for which the criterion must be satisfied before the
process can terminate.
ASINGULAR=r
ASING=r
specifies an absolute singularity criterion for the computation of the inertia (number of positive, negative, and zero eigenvalues) of the Hessian and its projected forms. The default value is the square
root of the smallest positive double-precision value.
DAMPSTEP< =r >
specifies that the initial step length value ˛ .0/ for each line search (used by the QUANEW, CONGRA, or NEWRAP technique) cannot be larger than r times the step length value used in the former
iteration. If the DAMPSTEP option is specified but r is not specified, the default is r = 2. The DAMPSTEP= option can prevent the line-search algorithm from repeatedly stepping into regions where
some objective functions are difficult to compute or where they could lead to floating-point overflows
during the computation of objective functions and their derivatives. The DAMPSTEP= option can
save time-consuming function calls during the line searches of objective functions that result in very
small steps.
FCONV=r < n >
FTOL=r < n >
specifies a relative function convergence criterion:
For all techniques except NMSIMP, termination requires a small relative change of the function
value in successive iterations,
jf . .k/ / f . .k 1/ /j
r
max.jf . .k 1/ /j; FSIZE/
where FSIZE is defined by the FSIZE= option.
The same formula is used for the NMSIMP technique, but .k/ is defined as the vertex with the
lowest function value and .k 1/ is defined as the vertex with the highest function value in the
simplex.
The default is r D 10 FDIGITS , where FDIGITS is by default log10 fg and is the machine precision. Some procedures, such as the GLIMMIX procedure, enable you to change the value with
the FDIGITS= option in the PROC statement. The optional integer value n specifies the number of
successive iterations for which the criterion must be satisfied before the process can terminate.
486 F Chapter 19: Shared Concepts and Topics
FCONV2=r < n >
FTOL2=r < n >
specifies a second function convergence criterion:
For all techniques except NMSIMP, termination requires a small predicted reduction,
df .k/ f .
.k/
/
f.
.k/
C s.k/ /
of the objective function. The predicted reduction
1 .k/0 .k/ .k/
0
df .k/ D g.k/ s.k/
s H s
2
1 .k/0 .k/
D
s g r
2
is computed by approximating the objective function f by the first two terms of the Taylor series
and substituting the Newton step,
s.k/ D
ŒH.k/ 
1 .k/
g
For the NMSIMP technique, termination requires a small standard deviation of the function
.k/
values of the p C 1 simplex vertices l , l D 0; : : : ; p,
s
i2
1 Xh
.k/
f . l / f . .k/ / r
nC1
l
.k/
1 P
.k/ , the
where f .
D pC1
l f . l /. If there are pact boundary constraints active at
mean and standard deviation are computed only for the n C 1 pact unconstrained vertices.
.k/ /
The default value is r = 1E–6 for the NMSIMP technique and r = 0 otherwise. The optional integer
value n specifies the number of successive iterations for which the criterion must be satisfied before
the process can terminate.
FSIZE=r
specifies the FSIZE parameter of the relative function and relative gradient termination criteria. The
default value is r = 0. For more details, see the FCONV= and GCONV= options.
GCONV=r < n >
GTOL=r < n >
specifies a relative gradient convergence criterion:
For all techniques except CONGRA and NMSIMP, termination requires that the normalized
predicted function reduction be small,
g. .k/ /0 ŒH.k/  1 g. .k/ /
r
max.jf . .k/ /j; FSIZE/
where FSIZE is defined by the FSIZE= option. For the CONGRA technique (where a reliable
Hessian estimate H is not available), the following criterion is used:
k g.
.k/
k g.
/ g.
k22 k s. .k/ / k2
r
1/ / k max.jf . .k/ /j; FSIZE/
2
.k/ /
.k
This criterion is not used by the NMSIMP technique.
The default value is r = 1E–8. The optional integer value n specifies the number of successive iterations for which the criterion must be satisfied before the process can terminate.
Syntax: NLOPTIONS Statement F 487
GCONV2=r < n >
GTOL2=r < n >
specifies another relative gradient convergence criterion:
For least squares problems and the TRUREG, LEVMAR, NRRIDG, and NEWRAP techniques,
the following criterion of Browne (1982) is used:
jgj . .k/ /j
max q
r
j
.k/
.k/
f.
/Hj;j
This criterion is not used by the other techniques.
The default value is r = 0. The optional integer value n specifies the number of successive iterations
for which the criterion must be satisfied before the process can terminate.
HESCAL=0 | 1 | 2 | 3
HS=0 | 1 | 2 | 3
specifies the scaling version of the Hessian (or crossproduct Jacobian) matrix used in NRRIDG,
TRUREG, LEVMAR, NEWRAP, or DBLDOG optimization.
If HS is not equal to 0, the first iteration and each restart iteration set the diagonal scaling matrix
.0/
D .0/ D diag.di /:
.0/
di
D
q
.0/
max.jHi;i j; /
.0/
where Hi;i are the diagonal elements of the Hessian (or crossproduct Jacobian). In every other
.0/
iteration, the diagonal scaling matrix D .0/ D diag.di / is updated depending on the HS option:
HS=0
specifies that no scaling be done.
HS=1
specifies the Moré (1978) scaling update:
q
.kC1/
.k/
.k/
di
D max di ; max.jHi;i j; /
HS=2
specifies the Dennis, Gay, and Welsch (1981) scaling update:
q
.k/
.kC1/
.k/
di
D max 0:6 di ; max.jHi;i j; /
HS=3
specifies that di be reset in each iteration:
q
.kC1/
.k/
di
D max.jHi;i j; /
In each scaling update, is the relative machine precision. The default value is HS=0. Scaling of the
Hessian can be time-consuming in the case where general linear constraints are active.
488 F Chapter 19: Shared Concepts and Topics
INHESSIAN< =r >
INHESS< =r >
specifies how the initial estimate of the approximate Hessian is defined for the quasi-Newton techniques QUANEW and DBLDOG. There are two alternatives:
If you do not use the r specification, the initial estimate of the approximate Hessian is set to the
Hessian at .0/ .
If you do use the r specification, the initial estimate of the approximate Hessian is set to the
multiple of the identity matrix rI.
By default (if you do not specify the option INHESSIAN=r ), the initial estimate of the approximate
Hessian is set to the multiple of the identity matrix rI, where the scalar r is computed from the
magnitude of the initial gradient.
INSTEP=r
SALPHA=r
RADIUS=r
reduces the length of the first trial step during the line search of the first iterations. For highly nonlinear
objective functions, such as the EXP function, the default initial radius of the trust-region algorithm
TRUREG or DBLDOG or the default step length of the line-search algorithms can result in arithmetic
overflows. If this occurs, you should specify decreasing values of 0 < r < 1 such as INSTEP=1E–1,
INSTEP=1E–2, INSTEP=1E–4, and so on, until the iteration starts successfully.
For trust-region algorithms (TRUREG or DBLDOG), the INSTEP= option specifies a factor r >
0 for the initial radius .0/ of the trust region. The default initial trust-region radius is the length
of the scaled gradient. This step corresponds to the default radius factor of r = 1.
For line-search algorithms (NEWRAP, CONGRA, or QUANEW), the INSTEP= option specifies
an upper bound for the initial step length for the line search during the first five iterations. The
default initial step length is r = 1.
For the Nelder-Mead simplex algorithm, by using TECH=NMSIMP, the INSTEP=r option defines the size of the start simplex.
LCDEACT=r
LCD=r
specifies a threshold r for the Lagrange multiplier that determines whether an active inequality constraint remains active or can be deactivated. For maximization, r must be greater than zero; for
minimization, r must be smaller than zero. An active inequality constraint can be deactivated only if
its Lagrange multiplier is less than the threshold value. The default value is
r D ˙ min.0:01; max.0:1 ABSGCONV; 0:001 gmax.k/ //
where “+” is for maximization, “–” is for minimization, ABSGCONV is the value of the absolute
gradient criterion, and gmax.k/ is the maximum absolute element of the gradient or the projected
gradient.
Syntax: NLOPTIONS Statement F 489
LCEPSILON=r
LCEPS=r
LCE=r
specifies the range r for active and violated boundary constraints, where r 0. If the point
satisfies the following condition, the constraint i is recognized as an active constraint:
j
k
X
aij
.k/
j
.k/
bi j r .jbi j C 1/
j D1
Otherwise, the constraint i is either an inactive inequality or a violated inequality or equality constraint. The default value is r = 1E–8. During the optimization process, the introduction of rounding
errors can force the optimization to increase the value of r by a factor of 10k for some k > 0. If this
happens, it is indicated by a message displayed in the log.
LCSINGULAR=r
LCSING=r
LCS=r
specifies a criterion r, where r 0, that is used in the update of the QR decomposition and that
determines whether an active constraint is linearly dependent on a set of other active constraints. The
default value is r = 1E–8. The larger r becomes, the more the active constraints are recognized as
being linearly dependent. If the value of r is larger than 0.1, it is reset to 0.1.
LINESEARCH=i
LIS=i
specifies the line-search method for the CONGRA, QUANEW, and NEWRAP optimization techniques. See Fletcher (1987) for an introduction to line-search techniques. The value of i can be
1; : : : ; 8 as follows. The default is LIS=2.
LIS=1
specifies a line-search method that needs the same number of function and gradient
calls for cubic interpolation and cubic extrapolation; this method is similar to one
used by the Harwell subroutine library.
LIS=2
specifies a line-search method that needs more function than gradient calls for
quadratic and cubic interpolation and cubic extrapolation; this method is implemented as shown in Fletcher (1987) and can be modified to an exact line search by
using the LSPRECISION= option. This is the default.
LIS=3
specifies a line-search method that needs the same number of function and gradient
calls for cubic interpolation and cubic extrapolation; this method is implemented
as shown in Fletcher (1987) and can be modified to an exact line search by using
the LSPRECISION= option.
LIS=4
specifies a line-search method that needs the same number of function and gradient
calls for stepwise extrapolation and cubic interpolation.
LIS=5
specifies a line-search method that is a modified version of LIS=4.
LIS=6
specifies a golden-section line search (Polak 1971), which uses only function values for linear approximation.
LIS=7
specifies a bisection line search (Polak 1971), which uses only function values for
linear approximation.
490 F Chapter 19: Shared Concepts and Topics
LIS=8
specifies the Armijo line-search technique (Polak 1971), which uses only function
values for linear approximation.
LSPRECISION=r
LSP=r
specifies the degree of accuracy that should be obtained by the line-search algorithms LIS=2 and
LIS=3. Usually an imprecise line search is inexpensive and successful. For more difficult optimization
problems, a more precise and expensive line search might be necessary (Fletcher 1987). The LIS=2
line-search method (which is the default for the NEWRAP, QUANEW, and CONGRA techniques)
and the LIS=3 line-search method approach exact line search for small LSPRECISION= values. If
you have numerical problems, try to decrease the LSPRECISION= value to obtain a more precise line
search. The default values are shown in Table 19.29.
Table 19.29 Default Values for Line-Search Precision
TECH=
UPDATE=
LSP Default
QUANEW
QUANEW
CONGRA
NEWRAP
DBFGS, BFGS
DDFP, DFP
All
No update
r
r
r
r
= 0.4
= 0.06
= 0.1
= 0.9
For more details, see Fletcher (1987).
MAXFUNC=i
MAXFU=i
specifies the maximum number i of function calls in the optimization process. The default values are
as follows:
125 for the TRUREG, NRRIDG, NEWRAP, and LEVMAR techniques
500 for the QUANEW and DBLDOG techniques
1000 for the CONGRA technique
3000 for the NMSIMP technique
Optimization can terminate only after completing a full iteration. Therefore, the number of function
calls that are actually performed can exceed the number that is specified by the MAXFUNC= option.
MAXITER=i
MAXIT=i
specifies the maximum number i of iterations in the optimization process. The default values are as
follows:
50 for the TRUREG, NRRIDG, NEWRAP, and LEVMAR techniques
200 for the QUANEW and DBLDOG techniques
400 for the CONGRA technique
1000 for the NMSIMP technique
These default values are also valid when i is specified as a missing value.
Syntax: NLOPTIONS Statement F 491
MAXSTEP=r < n >
specifies an upper bound for the step length of the line-search algorithms during the first n iterations.
By default, r is the largest double-precision value and n is the largest integer available. Setting this option can improve the speed of convergence for the CONGRA, QUANEW, and NEWRAP techniques.
MAXTIME=r
specifies an upper limit of r seconds of CPU time for the optimization process. The default value is the
largest floating-point double representation of your computer. The time specified by the MAXTIME=
option is checked only once at the end of each iteration. Therefore, the actual running time can be
much longer than that specified by the MAXTIME= option. The actual running time includes the rest
of the time needed to finish the iteration and the time needed to generate the output of the results.
MINITER=i
MINIT=i
specifies the minimum number of iterations. The default value is 0. If you request more iterations
than are actually needed for convergence to a stationary point, the optimization algorithms can behave
strangely. For example, the effect of rounding errors can prevent the algorithm from continuing for
the required number of iterations.
MSINGULAR=r
MSING=r
specifies a relative singularity criterion r, where r > 0, for the computation of the inertia (number of
positive, negative, and zero eigenvalues) of the Hessian and its projected forms. The default value is
1E–12.
NOPRINT
suppresses output that is related to optimization, such as the iteration history. This option, along
with all NLOPTIONS statement options for displayed output, are ignored by the GLIMMIX and
HPMIXED procedures.
PALL
displays all optional output for optimization. This option is supported only by the CALIS and SURVEYPHREG procedures.
PHISTORY
PHIST
displays the optimization history. The PHISTORY option is implied if the PALL option is specified.
The PHISTORY option is supported only by the CALIS and SURVEYPHREG procedures.
RESTART=i
REST=i
specifies that the QUANEW or CONGRA technique is restarted with a steepest search direction after
at most i iterations, where i > 0. Default values are as follows:
When TECHNIQUE=CONGRA and UPDATE=PB, restart is performed automatically; so i is
not used.
When TECHNIQUE=CONGRA and UPDATE¤PB, i D min.10p; 80/, where p is the number
of parameters.
When TECHNIQUE=QUANEW, i is the largest integer available.
492 F Chapter 19: Shared Concepts and Topics
SINGULAR=r
SING=r
specifies the singularity criterion r, 0r 1, that is used for the inversion of the Hessian matrix. The
default value is 1E–8.
SOCKET=fileref
specifies the fileref that contains the information needed for remote monitoring.
TECHNIQUE=value
TECH=value
OMETHOD=value
OM=value
specifies the optimization technique. You can find additional information about choosing an optimization technique in the section “Choosing an Optimization Algorithm” on page 494. Valid values
for the TECHNIQUE= option are as follows:
CONGRA
performs a conjugate-gradient optimization, which can be more precisely specified with the
UPDATE= option and modified with the LINESEARCH= option. When you specify this option,
UPDATE=PB by default.
DBLDOG
performs a version of double-dogleg optimization, which can be more precisely specified with
the UPDATE= option. When you specify this option, UPDATE=DBFGS by default.
LEVMAR
performs a highly stable, but for large problems memory- and time-consuming, LevenbergMarquardt optimization technique, a slightly improved variant of the Moré (1978) implementation. You can also specify this technique with the alias LM or MARQUARDT. In the CALIS
procedure, this is the default optimization technique if there are fewer than 40 parameters to estimate. The GLIMMIX and HPMIXED procedures do not support this optimization technique.
NMSIMP
performs a Nelder-Mead simplex optimization. The CALIS procedure does not support this
optimization technique.
NONE
does not perform any optimization. This option can be used for the following:
– to perform a grid search without optimization
– to compute estimates and predictions that cannot be obtained efficiently with any of the
optimization techniques
– to obtain inferences for known values of the covariance parameters
NEWRAP
performs a Newton-Raphson optimization that combines a line-search algorithm with ridging.
The line-search algorithm LIS=2 is the default method.
NRRIDG
performs a Newton-Raphson optimization with ridging. This is the default optimization technique in the SURVEYPHREG procedure.
Syntax: NLOPTIONS Statement F 493
QUANEW
performs a quasi-Newton optimization, which can be defined more precisely with the UPDATE=
option and modified with the LINESEARCH= option.
TRUREG
performs a trust-region optimization.
UPDATE=method
UPD=method
specifies the update method for the quasi-Newton, double-dogleg, or conjugate-gradient optimization
technique. Not every update method can be used with each optimizer.
The following are the valid methods for the UPDATE= option:
BFGS
performs the original Broyden, Fletcher, Goldfarb, and Shanno (BFGS) update of the inverse
Hessian matrix.
DBFGS
performs the dual BFGS update of the Cholesky factor of the Hessian matrix. This is the default
update method.
DDFP
performs the dual Davidon, Fletcher, and Powell (DFP) update of the Cholesky factor of the
Hessian matrix.
DFP
performs the original DFP update of the inverse Hessian matrix.
PB
performs the automatic restart update method of Powell (1977) and Beale (1972).
FR
performs the Fletcher-Reeves update (Fletcher 1987).
PR
performs the Polak-Ribiere update (Fletcher 1987).
CD
performs a conjugate-descent update of Fletcher (1987).
VERSION=1 | 2
VS=1 | 2
specifies the version of the quasi-Newton optimization technique with nonlinear constraints.
VS=1 specifies the update of the vector as in Powell (1978b, a) (update like VF02AD).
VS=2 specifies the update of the vector as in Powell (1982b, a) (update like VMCWD).
The default is VERSION=2.
494 F Chapter 19: Shared Concepts and Topics
VSINGULAR=r
VSING=r
specifies a relative singularity criterion r, where r > 0, for the computation of the inertia (number of
positive, negative, and zero eigenvalues) of the Hessian and its projected forms. The default value is
r = 1E–8.
XCONV=r < n >
XTOL=r < n >
specifies the relative parameter convergence criterion:
For all techniques except NMSIMP, termination requires a small relative parameter change in
subsequent iterations:
.k 1/
.k/
j
j
j
.k/
.k 1/
j; XSIZE/
j j; j j
maxj j
max.j
r
For the NMSIMP technique, the same formula is used, but
lowest function value and
simplex.
.k 1/
j
.k/
j
is defined as the vertex with the
is defined as the vertex with the highest function value in the
The default value is r = 1E–8 for the NMSIMP technique and r = 0 otherwise. The optional integer
value n specifies the number of successive iterations for which the criterion must be satisfied before
the process can be terminated.
XSIZE=r
specifies the XSIZE parameter r of the relative parameter termination criterion, where r 0. The
default value is r = 0. For more details, see the XCONV= option.
Choosing an Optimization Algorithm
First- or Second-Order Algorithms
The factors that go into choosing a particular optimization technique for a particular problem are complex.
Trial and error can be involved.
For many optimization problems, computing the gradient takes more computer time than computing the
function value. Computing the Hessian sometimes takes much more computer time and memory than
computing the gradient, especially when there are many decision variables. Unfortunately, optimization
techniques that do not use some kind of Hessian approximation usually require many more iterations than
techniques that do use a Hessian matrix, and, as a result, the total run time of these techniques is often
longer. Techniques that do not use the Hessian also tend to be less reliable. For example, they can terminate
more easily at stationary points than at global optima.
Table 19.30 shows which derivatives are required for each optimization technique.
Choosing an Optimization Algorithm F 495
Table 19.30
Derivatives Required
Algorithm
First-Order
Second-Order
LEVMAR
TRUREG
NEWRAP
NRRIDG
QUANEW
DBLDOG
CONGRA
NMSIMP
x
x
x
x
x
x
x
-
x
x
x
x
-
The second-derivative methods TRUREG, NEWRAP, and NRRIDG are best for small problems where the
Hessian matrix is not expensive to compute. Sometimes the NRRIDG algorithm can be faster than the
TRUREG algorithm, but TRUREG can be more stable. The NRRIDG algorithm requires only one matrix
with p.p C 1/=2 double words; TRUREG and NEWRAP require two such matrices. Here, p denotes the
number of parameters in the optimization.
The first-derivative methods QUANEW and DBLDOG are best for medium-sized problems where the objective function and the gradient are much faster to evaluate than the Hessian. In general, the QUANEW
and DBLDOG algorithms require more iterations than TRUREG, NRRIDG, and NEWRAP, but each iteration can be much faster. The QUANEW and DBLDOG algorithms require only the gradient to update an
approximate Hessian, and they require slightly less memory than TRUREG or NEWRAP (essentially one
matrix with p.p C 1/=2 double words).
The first-derivative method CONGRA is best for large problems where the objective function and the gradient can be computed much faster than the Hessian and where too much memory is required to store the
(approximate) Hessian. In general, the CONGRA algorithm requires more iterations than QUANEW or
DBLDOG, but each iteration can be much faster. Because CONGRA requires only a factor of p doubleword memory, many large applications can be solved only by CONGRA.
The no-derivative method NMSIMP is best for small problems where derivatives are not continuous or are
very difficult to compute.
Each optimization method uses one or more convergence criteria that determine when it has converged. An
algorithm is considered to have converged when any one of the convergence criteria is satisfied. For example, under the default settings, the QUANEW algorithm will converge if ABSGCONV < 1E–5, FCONV <
10 FDIGITS , or GCONV < 1E–8.
Algorithm Descriptions
Trust Region Optimization (TRUREG)
The trust region method uses the gradient g. .k/ / and the Hessian matrix H. .k/ /; thus, it requires that the
objective function f . / have continuous first- and second-order derivatives inside the feasible region.
The trust region method iteratively optimizes a quadratic approximation to the nonlinear objective function
within a hyperelliptic trust region with radius  that constrains the step size that corresponds to the quality
of the quadratic approximation. The trust region method is implemented based on Dennis, Gay, and Welsch
(1981); Gay (1983) and Moré and Sorensen (1983).
496 F Chapter 19: Shared Concepts and Topics
The trust region method performs well for small- to medium-sized problems, and it does not need many
function, gradient, and Hessian calls. However, if the computation of the Hessian matrix is computationally
expensive, one of the (dual) quasi-Newton or conjugate gradient algorithms might be more efficient.
Newton-Raphson Optimization with Line Search (NEWRAP)
The NEWRAP technique uses the gradient g. .k/ / and the Hessian matrix H. .k/ /; thus, it requires that
the objective function have continuous first- and second-order derivatives inside the feasible region. If
second-order derivatives are computed efficiently and precisely, the NEWRAP method can perform well for
medium-sized to large problems, and it does not need many function, gradient, and Hessian calls.
This algorithm uses a pure Newton step when the Hessian is positive definite and when the Newton step
reduces the value of the objective function successfully. Otherwise, a combination of ridging and line
search is performed to compute successful steps. If the Hessian is not positive definite, a multiple of the
identity matrix is added to the Hessian matrix to make it positive definite (Eskow and Schnabel 1991).
In each iteration, a line search is performed along the search direction to find an approximate optimum of
the objective function. The default line-search method uses quadratic interpolation and cubic extrapolation
(LIS=2).
Newton-Raphson Ridge Optimization (NRRIDG)
The NRRIDG technique uses the gradient g. .k/ / and the Hessian matrix H. .k/ /; thus, it requires that
the objective function have continuous first- and second-order derivatives inside the feasible region.
This algorithm uses a pure Newton step when the Hessian is positive definite and when the Newton step
reduces the value of the objective function successfully. If at least one of these two conditions is not satisfied,
a multiple of the identity matrix is added to the Hessian matrix.
The NRRIDG method performs well for small- to medium-sized problems, and it does not require many
function, gradient, and Hessian calls. However, if the computation of the Hessian matrix is computationally
expensive, one of the (dual) quasi-Newton or conjugate gradient algorithms might be more efficient.
Because the NRRIDG technique uses an orthogonal decomposition of the approximate Hessian, each iteration of NRRIDG can be slower than that of the NEWRAP technique, which works with a Cholesky
decomposition. Usually, however, NRRIDG requires fewer iterations than NEWRAP.
Quasi-Newton Optimization (QUANEW)
The (dual) quasi-Newton method uses the gradient g. .k/ /, and it does not need to compute second-order
derivatives because they are approximated. It works well for medium-sized to moderately large optimization
problems, where the objective function and the gradient are much faster to compute than the Hessian. However, in general, it requires more iterations than the TRUREG, NEWRAP, and NRRIDG techniques, which
compute second-order derivatives. QUANEW is the default optimization algorithm because it provides an
appropriate balance between the speed and stability required for most nonlinear mixed model applications.
The QUANEW technique is one of the following, depending upon the value of the UPDATE= option:
the original quasi-Newton algorithm, which updates an approximation of the inverse Hessian
the dual quasi-Newton algorithm, which updates the Cholesky factor of an approximate Hessian (this
is the default)
You can specify four update formulas with the UPDATE= option:
Choosing an Optimization Algorithm F 497
DBFGS performs the dual Broyden, Fletcher, Goldfarb, and Shanno (BFGS) update of the Cholesky
factor of the Hessian matrix. This is the default.
DDFP performs the dual Davidon, Fletcher, and Powell (DFP) update of the Cholesky factor of the
Hessian matrix.
BFGS performs the original BFGS update of the inverse Hessian matrix.
DFP performs the original DFP update of the inverse Hessian matrix.
In each iteration, a line search is performed along the search direction to find an approximate optimum.
The default line-search method uses quadratic interpolation and cubic extrapolation to obtain a step size
˛ that satisfies the Goldstein conditions. One of the Goldstein conditions can be violated if the feasible
region defines an upper limit of the step size. Violating the left-side Goldstein condition can affect the
positive definiteness of the quasi-Newton update. In that case, either the update is skipped or the iterations
are restarted with an identity matrix, resulting in the steepest descent or ascent search direction. You can
specify line-search algorithms other than the default with the LIS= option.
The QUANEW algorithm uses its own line-search technique. Of the options and parameters that control the
line search for other algorithms, only the INSTEP= option applies here. In several applications, large steps
in the first iterations are troublesome. You can use the INSTEP= option to impose an upper bound for the
step size ˛ during the first five iterations. You can also use the INHESSIAN= option to specify a different
starting approximation for the Hessian. If you specify only the INHESSIAN option, the Cholesky factor
of a (possibly ridged) finite-difference approximation of the Hessian is used to initialize the quasi-Newton
update process.
Double-Dogleg Optimization (DBLDOG)
The double-dogleg optimization method combines the ideas of the quasi-Newton and trust region methods. In each iteration, the double-dogleg algorithm computes the step s.k/ as the linear combination of the
.k/
.k/
steepest descent or ascent search direction s1 and a quasi-Newton search direction s2 ,
.k/
.k/
s.k/ D ˛1 s1 C ˛2 s2
The step is requested to remain within a prespecified trust region radius; see Fletcher (1987, p, 107). Thus,
the DBLDOG subroutine uses the dual quasi-Newton update but does not perform a line search. You can
specify two update formulas with the UPDATE= option:
DBFGS performs the dual Broyden, Fletcher, Goldfarb, and Shanno update of the Cholesky factor of
the Hessian matrix. This is the default.
DDFP performs the dual Davidon, Fletcher, and Powell update of the Cholesky factor of the Hessian
matrix.
The double-dogleg optimization technique works well for medium-sized to moderately large optimization problems, where the objective function and the gradient are much faster to compute than the Hessian. The implementation is based on Dennis and Mei (1979); Gay (1983), but it is extended for dealing
with boundary and linear constraints. The DBLDOG technique generally requires more iterations than the
TRUREG, NEWRAP, and NRRIDG techniques, which require second-order derivatives; however, each of
the DBLDOG iterations is computationally cheap. Furthermore, the DBLDOG technique requires only
gradient calls for the update of the Cholesky factor of an approximate Hessian.
498 F Chapter 19: Shared Concepts and Topics
Conjugate Gradient Optimization (CONGRA)
Second-order derivatives are not required by the CONGRA algorithm and are not even approximated. The
CONGRA algorithm can be expensive in function and gradient calls, but it requires only O.p/ memory for
unconstrained optimization. In general, many iterations are required to obtain a precise solution, but each
of the CONGRA iterations is computationally cheap. You can specify four different update formulas for
generating the conjugate directions by using the UPDATE= option:
PB performs the automatic restart update method of Powell (1977) and Beale (1972). This is the
default.
FR performs the Fletcher-Reeves update (Fletcher 1987).
PR performs the Polak-Ribiere update (Fletcher 1987).
CD performs a conjugate-descent update of Fletcher (1987).
The default often behaves best for typical examples, whereas UPDATE=CD can perform poorly.
The CONGRA subroutine should be used for optimization problems with large p. For the unconstrained
or boundary-constrained case, CONGRA requires only O.p/ bytes of working memory, whereas all other
optimization methods require order O.p 2 / bytes of working memory. During p successive iterations, uninterrupted by restarts or changes in the working set, the conjugate gradient algorithm computes a cycle of p
conjugate search directions. In each iteration, a line search is performed along the search direction to find an
approximate optimum of the objective function. The default line-search method uses quadratic interpolation
and cubic extrapolation to obtain a step size ˛ that satisfies the Goldstein conditions. One of the Goldstein
conditions can be violated if the feasible region defines an upper limit for the step size. Other line-search
algorithms can be specified with the LIS= option.
Nelder-Mead Simplex Optimization (NMSIMP)
The Nelder-Mead simplex method does not use any derivatives and does not assume that the objective
function has continuous derivatives. The objective function itself needs to be continuous. This technique
is quite expensive in the number of function calls, and it might be unable to generate precise results for
p 40.
The original Nelder-Mead simplex algorithm is implemented and extended to boundary constraints. This
algorithm does not compute the objective for infeasible points, but it changes the shape of the simplex adapting to the nonlinearities of the objective function, which contributes to an increased speed of convergence.
It uses a special termination criterion.
SLICE Statement
This statement applies to the following SAS/STAT procedures:
GENMOD, GLIMMIX, LIFEREG, LOGISTIC, MIXED, ORTHOREG, PHREG, PLM, PROBIT, SURVEYLOGISTIC, SURVEYPHREG, and SURVEYREG. It also applies to the RELIABILITY procedure in
SAS/QC software.
SLICE Statement F 499
The SLICE statement is similar to the LSMEANS statement. You use it to perform inferences on model
effects that consist entirely of classification variables. With the SLICE statement, these effects must be
higher-order effects of at least two classification variables. The effect is then partitioned into subsets that correspond to variables used in forming the effect. You can use the same options as you use for the LSMEANS
statement to perform an analysis for the partitions. This analysis is also known as an analysis of simple
effects (Winer 1971).
By default, the interaction effect is partitioned by all main effects. For example, the following statements
produce simple-effect differences among the A levels for each level of B and simple-effect differences among
the B levels for each level of A:
class a b;
model y = a b a*b;
slice a*b / diff nof;
For example, if the model-effect is a three-way interaction effect, the default output includes comparisons
of the two-way interaction means.
Suppose, for example, that the interaction effect A*B is significant in your analysis and that you want to test
the effect of A for each level of B. The appropriate statement is
slice A*B / sliceBy = B;
This produces an F test for each level of B that compares the equality of the levels of A.
For example, assume that in a balanced design factors A and B have a = 4 and b = 3 levels, respectively.
Consider the following statements:
class a b;
model y = a b a*b;
slice a*b / sliceby=a diff;
The SLICE statement produces four F tests, one per level of A. The first of these tests is constructed by
extracting the three rows that correspond to the first level of A from the coefficient matrix for the A*B
.1/ .2/
.3/
interaction. Call this matrix La1 and its rows la1 , la1 , and la1 . The slice tests the two-degrees-of-freedom
hypothesis
8 < l.1/ l.2/ ˇ D 0
a1
a1
H W .1/ .3/ : l
la1 ˇ D 0
a1
In a balanced design, where ij denotes the mean response if A is at level i and B is at level j, this hypothesis
is equivalent to H W 11 D 12 D 13 . The DIFF option considers the three rows of La1 in turn and
performs tests of the difference between pairs of rows. By default, all pairwise differences within the subset
of L are considered; in the example this corresponds to tests of the form
.1/
.2/
H W la1 la1 ˇ D 0
.1/
.3/
H W la1 la1 ˇ D 0
.2/
.3/
H W la1 la1 ˇ D 0
In the example, with a = 4 and b = 3, this produces four sets of least squares means differences. Within each
set, factor A is held fixed at a particular level and each set consists of three comparisons.
500 F Chapter 19: Shared Concepts and Topics
Syntax: SLICE Statement
SLICE model-effect < / options > ;
You can specify all options of the LSMEANS statement in the SLICE statement. The philosophy of the
SLICE statement is to apply the analysis according to the options to the subsets of the L matrix that correspond to chosen partitions.
The following behavior differences between the SLICE and the LSMEANS statement are noteworthy:
The specification of the model-effect is optional in the LSMEANS statement and required in the
SLICE statement.
Only a single SLICE model-effect can be specified before the option slash (/). However, you can
specify multiple partitioning rules with the SLICEBY option.
The MEANS option is the default for most procedures in the LSMEANS statement. For the SLICE
statement, the default is the NOMEANS option.
Also, the three generalized linear modeling options: EXP, ILINK, and ODDSRATIO in the SLICE statement are additionally supported by PROC GLIMMIX and by PROC PLM when it is used to perform statistical analyses on item stores that were created by PROC GLIMMIX.
In addition to the options in the LSMEANS statement, you can specify the following options in the SLICE
statement after the slash (/):
SLICEBY < = > slice-specification
SIMPLE < = > slice-specification
SLICEBY(slice-specification < , slice-specification < , : : : > >)
SIMPLE(slice-specification < , slice-specification < , : : : > >)
determines how to construct the partition of the least squares means for the model-effect. A slicespecification consists of an effect name followed by an optional list of formatted values. For example,
the following statements creates partitions of the A*B interaction effect for all levels of variable A:
class a b;
model y = a b a*b;
slice a*b / sliceby=a;
The following statements produces two partitions of the interaction:
class a b;
model y = a b a*b;
slice a*b / sliceby(b='2' a='1') diff;
In the first partition the variable B takes on formatted value ‘2’. In the second partition the variable A
takes on the formatted value ‘1’.
STORE Statement F 501
NOF
suppresses the F test for testing the mutual equality of the estimable functions in the partition.
ODS Table Names: SLICE Statement
Each table created by the SLICE statement has a name associated with it, and you can use this name to
refer to the table when using the Output Delivery System (ODS) to select tables and create output data sets.
These names are listed in Table 19.31. For more information about ODS, see Chapter 20, “Using the Output
Delivery System.”
Table 19.31 ODS Tables Produced by the SLICE statement
Table Name
Description
Required Option
Coef
Slices
SliceDiffs
L matrix coefficients
LS-means slices
Simple differences of LS-means slices
SliceLines
SliceTests
Lines display for LS-means slices
Tests for LS-means slices
E
MEANS
DIFF or ADJUST= or
STEPDOWN or NOF
LINES
Default
STORE Statement
This statement applies to the following SAS/STAT procedures:
GENMOD, GLIMMIX, GLM, GLMSELECT, LOGISTIC, MIXED, ORTHOREG, PHREG, PROBIT,
SURVEYLOGISTIC, SURVEYPHREG, and SURVEYREG. It also applies to the RELIABILITY procedure in SAS/QC software.
The STORE statement requests that the procedure save the context and results of the statistical analysis into
an item store. An item store is a binary file format that cannot be modified by the user. The contents of the
item store can be processed with the PLM procedure. One example of item store technology is to perform
a time-consuming analysis and to store its results by using the STORE statement. At a later time you can
then perform specific statistical analysis tasks based on the saved results of the previous analysis, without
having to fit the model again. The following statements show an example in which a mixed model is fit with
the MIXED procedure and the postprocessing analysis is performed with the PLM procedure:
proc mixed data=MyBigDataSet;
class Env A B sub;
model y = A B x / ddfm=KenwardRoger;
random int A*B / sub=Env;
repeated / subject=Env*A*B type=AR(1);
store sasuser.mixed;
run;
502 F Chapter 19: Shared Concepts and Topics
proc plm restore=sasuser.mixed;
show cov Parms;
lsmeans A B / diff;
score data=NewData out=ScoreResults;
run;
The STORE statement in the PROC MIXED step requests that the MIXED procedure save those results
that are needed to perform statistical tasks with the PLM procedure. For example, the MIXED procedure
saves the necessary pieces of information that relate to the Kenward-Roger degree-of-freedom method. The
results from the LSMEANS statement in the PROC PLM step thus apply this technique for calculating
denominator degrees of freedom. The SHOW statement in the PLM procedure reveals the contents of the
item store in terms of ODS tables, and the SCORE statement computes predicted values in a new data set.
For more information about postprocessing tasks based on item stores, see the documentation for the PLM
procedure.
Syntax: STORE Statement
STORE < OUT= >item-store-name < / LABEL=‘label’ > ;
The item-store-name is a usual one- or two-level SAS name, like the names that are used for SAS data sets.
If you specify a one-level name, then the item store resides in the WORK library and is deleted at the end of
the SAS session. Since item stores usually are used to perform postprocessing tasks, typical usage specifies
a two-level name of the form libname.membername.
If an item store by the same name as specified in the STORE statement already exists, the existing store is
replaced.
You can add a custom label with the LABEL= option in the STORE statement after the slash (/). When
the PLM procedure processes an item store, the label appears in the PROC PLM output along with other
identifying information.
TEST Statement
This statement documentation applies to the following procedures:
LIFEREG, ORTHOREG, PLM, PROBIT, SURVEYPHREG, and SURVEYREG. It also applies to the RELIABILITY procedure in SAS/QC software.
The TEST statement enables you to perform F tests for model effects that test Type I, II, or Type III hypotheses. See Chapter 15, “The Four Types of Estimable Functions,” for details about the construction of
Type I, II, and III estimable functions.
Syntax: TEST Statement F 503
Syntax: TEST Statement
TEST < model-effects > < / options > ;
Table 19.32 summarizes options in the TEST statement.
Table 19.32 TEST Statement Options
Option
Description
CHISQ
DDF=
E
E1
E2
E3
HTYPE=
INTERCEPT
Requests chi-square tests
Specifies denominator degrees of freedom for fixed effects
Requests Type I, Type II, and Type III coefficients
Requests Type I coefficients
Requests Type II coefficients
Requests Type III coefficients
Indicates the type of hypothesis test to perform
Adds a row that corresponds to the overall intercept
You can specify the following options in the TEST statement after the slash (/):
CHISQ
requests that chi-square tests be performed for the relevant effects in addition to the F tests. Type III
tests are the default; you can produce the Type I and Type II tests by using the HTYPE= option. This
option has no effect when the procedure produces chi-square statistics by default.
DDF=value-list
DF=value-list
specifies the denominator degrees of freedom for the fixed effects. The value-list specification is a list
of numbers or missing values (.) separated by commas. The order of degrees of freedom should match
the order of the fixed effects that are specified in the TEST statement; otherwise it should match the
order in which the effects appear in the “Type III Tests of Fixed Effects” table. If you want to retain
the default degrees of freedom for a particular effect, use a missing value for its location in the list. In
the following example, the first TEST statement assigns 3 denominator degrees of freedom to A and
4.7 to A*B, while those for B remain the same, and the second TEST statement assigns 5 denominator
degrees of freedom to A and uses the default degrees of freedom for B.
model Y = A B A*B;
test / ddf=3,.,4.7;
test B A / ddf=.,5;
E
requests that Type I, Type II, and Type III L matrix coefficients be displayed for all relevant effects.
E1 | EI
requests that Type I L matrix coefficients be displayed for all relevant effects.
504 F Chapter 19: Shared Concepts and Topics
E2 | EII
requests that Type II L matrix coefficients be displayed for all relevant effects.
E3 | EIII
requests that Type III L matrix coefficients be displayed for all relevant effects.
HTYPE=value-list
indicates the type of hypothesis test to perform on the fixed effects. Valid entries for values in the
value-list are 1, 2, and 3, which correspond to Type I, Type II, and Type III tests, respectively. The
default value is 3.
INTERCEPT
INT
adds a row to the tables for Type I, II, and III tests that correspond to the overall intercept.
ODS Table Names: TEST Statement
Each table created by the TEST statement has a name associated with it, and you can use this name to
refer to the table when using the Output Delivery System (ODS) to select tables and create output data sets.
These names are listed in Table 19.33. For more information about ODS, see Chapter 20, “Using the Output
Delivery System.”
Table 19.33 ODS Tables Produced by the TEST statement
Table Name
Description
Required Option
Coef
Tests1
Tests2
Tests3
L matrix coefficients
Type I tests of fixed effects
Type II tests of fixed effects
Type III tests of fixed effects
E
HTYPE=1
HTYPE=2
Default
Programming Statements
This section applies to the following procedures:
CALIS, GLIMMIX, MCMC, NLIN, NLMIXED, PHREG, and SURVEYPHREG.
The majority of the SAS/STAT modeling procedures can take advantage of the fact that the statistical model
can easily be translated into programming syntax (statements and options). However, several procedures
require additional flexibility in specifying models—for example, when the model contains general nonlinear
functions, when it is necessary to specify complicated restrictions, or when user-supplied expressions need
to be evaluated. Procedures that are listed at the beginning of the section support—in addition to the usual
procedure statements and options—programming statements that can be used in the SAS DATA step.
The following are valid statements:
Programming Statements F 505
ABORT;
ARRAY arrayname < [ dimensions ] > < $ > < variables-and-constants >;
CALL name < (expression < , expression . . . >) >;
DELETE;
DO < variable = expression < TO expression > < BY expression > >
< , expression < TO expression > < BY expression > > . . .
< WHILE expression > < UNTIL expression >;
END;
GOTO statement-label;
IF expression;
IF expression THEN program-statement;
ELSE program-statement;
variable = expression;
variable + expression;
LINK statement-label;
PUT < variable > < = > . . . ;
RETURN;
SELECT < (expression) >;
STOP;
SUBSTR(variable, index, length)= expression;
WHEN (expression)program-statement;
OTHERWISE program-statement;
For the most part, these programming statements work the same as they do in the SAS DATA step, as
documented in SAS Language Reference: Concepts. However, there are several differences:
The ABORT statement does not allow any arguments.
The DO statement does not allow a character index variable. Thus
do i = 1,2,3;
is supported, whereas the following statement is not supported:
do i = 'A','B','C';
Not all procedures support LAG functionality. For example, the GLIMMIX procedure does not support lags.
The PUT statement, used mostly for program debugging, supports only some of the features of the
DATA step PUT statement, and it has some features that are not available with the DATA step PUT
statement:
– The PUT statement does not support line pointers, factored lists, iteration factors, overprinting,
_INFILE_, the colon (:) format modifier, or “$”.
– The PUT statement does support expressions, but the expression must be enclosed in parentheses. For example, the following statement displays the square root of x:
506 F Chapter 19: Shared Concepts and Topics
put (sqrt(x));
– The PUT statement supports the item _PDV_ to display a formatted listing of all variables in the
program. For example:
put _pdv_;
The WHEN and OTHERWISE statements enable you to specify more than one target statement. That
is, DO/END groups are not necessary for multiple-statement WHENs. For example, the following
syntax is valid:
select;
when (exp1) stmt1;
stmt2;
when (exp2) stmt3;
stmt4;
end;
The LINK statement is used in a program to jump immediately to the label statement_label and to
continue program execution at that point. It is not used to specify a link function in a generalized
linear model.
Please consult the individual chapters for other, procedure-specific differences between programming statements and the SAS DATA step and for procedure-specific details, limitations, and rules.
When coding your programming statements, avoid defining variables that begin with an underscore (_),
because they might conflict with internal variables that are created by procedures that support programming
statements.
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Beale, E. M. L. (1972), “A Derivation of Conjugate Gradients,” in F. A. Lootsma, ed., Numerical Methods
for Nonlinear Optimization, London: Academic Press.
Browne, M. W. (1982), “Covariance Structures,” in D. M. Hawkins, ed., Topics in Applied Multivariate
Analysis, 72–141, Cambridge: Cambridge University Press.
Dennis, J. E., Gay, D. M., and Welsch, R. E. (1981), “An Adaptive Nonlinear Least-Squares Algorithm,”
ACM Transactions on Mathematical Software, 7, 348–368.
Dennis, J. E. and Mei, H. H. W. (1979), “Two New Unconstrained Optimization Algorithms Which Use
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Edwards, D. and Berry, J. J. (1987), “The Efficiency of Simulation-Based Multiple Comparisons,” Biometrics, 43, 913–928.
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Fletcher, R. (1987), Practical Methods of Optimization, Second Edition, Chichester, UK: John Wiley &
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Fox, J. (1987), Sociological Methodology, chapter Effect Displays for Generalized Linear Models, 347–361,
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Frankel, S. A. (1961), “Statistical Design of Experiments for Process Development of MBT,” Rubber Age,
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Games, P. A. and Howell, J. F. (1976), “Pairwise Multiple Comparison Procedures with Unequal n’s and/or
Variances: A Monte Carlo Study,” Journal of Educational Statistics, 1, 113–125.
Gay, D. M. (1983), “Subroutines for Unconstrained Minimization,” ACM Transactions on Mathematical
Software, 9, 503–524.
Guirguis, G. and Tobias, R. D. (2004), “On the Computation of the Distribution for the Analysis of Means,”
Communications in Statistics: Simulation and Computation, 33, 861–888.
Hastie, T., Tibshirani, R., and Friedman, J. (2001), The Elements of Statistical Learning, New York:
Springer-Verlag.
Holm, S. (1979), “A Simple Sequentially Rejective Multiple Test Procedure,” Scandinavian Journal of
Statistics, 6, 65–70.
Hsu, J. C. (1992), “The Factor Analytic Approach to Simultaneous Inference in the General Linear Model,”
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Journal of Computational and Graphical Statistics, 3, 143–161.
Kenward, M. G. and Roger, J. H. (1997), “Small Sample Inference for Fixed Effects from Restricted Maximum Likelihood,” Biometrics, 53, 983–997.
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Statistical Computing, 4, 553–572.
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Technometrics, 35, 61–71.
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Powell, M. J. D. (1978a), “Algorithms for Nonlinear Constraints That Use Lagrangian Functions,” Mathematical Programming, 14, 224–248.
Powell, M. J. D. (1978b), “A Fast Algorithm for Nonlinearly Constrained Optimization Calculations,” in
G. A. Watson, ed., Lecture Notes in Mathematics, volume 630, 144–175, Berlin: Springer-Verlag.
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and Multiple Tests Using the SAS System, Cary, NC: SAS Institute Inc.
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Subject Index
B-spline
spline basis (Shared Concepts), 408
B-spline basis
GLIMMIX procedure, 408
GLMSELECT procedure, 408
HPMIXED procedure, 408
LOGISTIC procedure, 408
ORTHOREG procedure, 408
PHREG procedure, 408
PLS procedure, 408
QUANTLIFE procedure, 408
QUANTREG procedure, 408
QUANTSELECT procedure, 408
ROBUSTREG procedure, 408
SURVEYLOGISTIC procedure, 408
SURVEYREG procedure, 408
bar (|) operator
Shared Concepts, 383
choosing optimization algorithm
Shared Concepts, 494
CLASS statement
Shared Concepts, 380
classification variables
Shared Concepts, 380
CODE statement
syntax (Shared Concepts), 391
collection effect
GLIMMIX procedure, 395
GLMSELECT procedure, 395
HPMIXED procedure, 395
LOGISTIC procedure, 395
ORTHOREG procedure, 395
PHREG procedure, 395
PLS procedure, 395
QUANTLIFE procedure, 395
QUANTREG procedure, 395
QUANTSELECT procedure, 395
ROBUSTREG procedure, 395
SURVEYLOGISTIC procedure, 395
SURVEYREG procedure, 395
conjugate
descent (GLIMMIX), 493
gradient (GLIMMIX), 492
conjugate gradient method
Shared Concepts, 498
continuous-by-class effects
Shared Concepts, 386
continuous-nesting-class effects
Shared Concepts, 385
convergence criterion
GLIMMIX procedure, 484, 486, 487, 494
crossed effects
Shared Concepts, 384
Davidon-Fletcher-Powell update, 493
double dogleg
method (GLIMMIX), 492
double-dogleg method
Shared Concepts, 497
effect parameterization
Shared Concepts, 387
effect plot
EFFECTPLOT statement, 411
EFFECT statement
collection effect (Shared Concepts), 395
lag effect (Shared Concepts), 395
multimember effect (Shared Concepts), 398
polynomial effect (Shared Concepts), 399
spline effect (Shared Concepts), 403
syntax (Shared Concepts), 393
EFFECTPLOT statement
ODS graph names, 422
syntax (Shared Concepts), 411
ESTIMATE statement
chi-bar-square statistic, 451
estimate-specification (Shared Concepts), 438
joint hypothesis tests with complex alternatives,
451
multiple comparison adjustment (Shared
Concepts), 440
positional and nonpositional syntax, 448
syntax (Shared Concepts), 438
Estimate-specification
ESTIMATE statement, 438
examples, GLIMMIX
multimember effect, 398
spline effect, 393
examples, GLMSELECT
multimember effect, 398
examples, HPMIXED
multimember effect, 398
examples, LOGISTIC
multimember effect, 398
examples, ORTHOREG
multimember effect, 398
examples, PHREG
multimember effect, 398
examples, PLS
multimember effect, 398
examples, QUANTLIFE
multimember effect, 398
examples, QUANTREG
multimember effect, 398
examples, QUANTSELECT
multimember effect, 398
examples, ROBUSTREG
multimember effect, 398
examples, SURVEYLOGISTIC
multimember effect, 398
examples, SURVEYREG
multimember effect, 398
first-order algorithm
Shared Concepts, 494
general effects
Shared Concepts, 386
GENMOD procedure
analysis of means, 461
diffogram, 464
observed margins, 462
ODS graph names, 422
GENMOD procedure, LSMEANS statement
ODS graph names, 468
ODS table names, 468
GLIMMIX procedure
analysis of means, 461
B-spline basis, 408
collection effect, 395
convergence criterion, 484, 486, 487, 494
diffogram, 464
functional convergence criteria, 485
Hessian scaling, 487
lag effect, 395
lag functionality, 505
line-search methods, 489
line-search precision, 490
multimember effect, 398
Natural cubic spline basis, 411
Newton-Raphson algorithm, 492
Newton-Raphson algorithm with ridging, 492
observed margins, 462
optimization technique, 492
polynomial effect, 399
remote monitoring, 492
spline bases, 406
spline effect, 403
TPF basis, 407
truncated power function basis, 407
GLIMMIX procedure, SLICE statement
ODS graph names, 468
GLM parameterization
Shared Concepts, 388
GLMSELECT procedure
B-spline basis, 408
collection effect, 395
lag effect, 395
multimember effect, 398
Natural cubic spline basis, 411
polynomial effect, 399
spline bases, 406
spline effect, 403
TPF basis, 407
truncated power function basis, 407
Hessian scaling
GLIMMIX procedure, 487
HPMIXED procedure
B-spline basis, 408
collection effect, 395
lag effect, 395
multimember effect, 398
Natural cubic spline basis, 411
polynomial effect, 399
spline bases, 406
spline effect, 403
TPF basis, 407
truncated power function basis, 407
interaction effects
Shared Concepts, 384
intercept
Shared Concepts, 383
lag effect
GLIMMIX procedure, 395
GLMSELECT procedure, 395
HPMIXED procedure, 395
LOGISTIC procedure, 395
ORTHOREG procedure, 395
PHREG procedure, 395
PLS procedure, 395
QUANTLIFE procedure, 395
QUANTREG procedure, 395
QUANTSELECT procedure, 395
ROBUSTREG procedure, 395
SURVEYLOGISTIC procedure, 395
SURVEYREG procedure, 395
lag functionality
GLIMMIX procedure, 505
levelization
Shared Concepts, 380
LIFEREG procedure
analysis of means, 461
chi-bar-square statistic, 451
diffogram, 464
joint hypothesis tests with complex alternatives,
451
observed margins, 462
positional and nonpositional syntax, 448
LIFEREG procedure, ESTIMATE statement
ODS table names, 452
LIFEREG procedure, LSMEANS statement
ODS graph names, 468
ODS table names, 468
line-search methods
GLIMMIX procedure, 489
LOGISTIC procedure
analysis of means, 461
B-spline basis, 408
chi-bar-square statistic, 451
collection effect, 395
diffogram, 464
joint hypothesis tests with complex alternatives,
451
lag effect, 395
multimember effect, 398
Natural cubic spline basis, 411
observed margins, 462
ODS graph names, 422
polynomial effect, 399
positional and nonpositional syntax, 448
spline bases, 406
spline effect, 403
TPF basis, 407
truncated power function basis, 407
LOGISTIC procedure, ESTIMATE statement
ODS table names, 452
LOGISTIC procedure, LSMEANS statement
ODS graph names, 468
ODS table names, 468
LSMEANS statement
analysis of means (Shared Concepts), 461
diffogram (Shared Concepts), 464
least squares means (Shared Concepts), 453
multiple comparison adjustment (Shared
Concepts), 455
observed margins (Shared Concepts), 462
syntax (Shared Concepts), 454
LSMESTIMATE statement
syntax (Shared Concepts), 471
main effects
Shared Concepts, 384
MIXED procedure
analysis of means, 461
diffogram, 464
observed margins, 462
MIXED procedure, SLICE statement
ODS graph names, 468
multimember effect
GLIMMIX procedure, 398
GLMSELECT procedure, 398
HPMIXED procedure, 398
LOGISTIC procedure, 398
ORTHOREG procedure, 398
PHREG procedure, 398
PLS procedure, 398
QUANTLIFE procedure, 398
QUANTREG procedure, 398
QUANTSELECT procedure, 398
ROBUSTREG procedure, 398
SURVEYLOGISTIC procedure, 398
SURVEYREG procedure, 398
Natural cubic spline
spline basis (Shared Concepts), 411
Natural cubic spline basis
GLIMMIX procedure, 411
GLMSELECT procedure, 411
HPMIXED procedure, 411
LOGISTIC procedure, 411
ORTHOREG procedure, 411
PHREG procedure, 411
PLS procedure, 411
QUANTLIFE procedure, 411
QUANTREG procedure, 411
QUANTSELECT procedure, 411
ROBUSTREG procedure, 411
SURVEYLOGISTIC procedure, 411
SURVEYREG procedure, 411
Nelder-Mead simplex
method (GLIMMIX), 492
Nelder-Mead simplex method
Shared Concepts, 498
nested effects
Shared Concepts, 385
nested versus crossed effects
Shared Concepts, 385
Newton-Raphson algorithm
GLIMMIX procedure, 492
Newton-Raphson algorithm with ridging
GLIMMIX procedure, 492
Newton-Raphson method
Shared Concepts, 496
Newton-Raphson with ridging
Shared Concepts, 496
NLOPTIONS statement
syntax (Shared Concepts), 482
ODS graph names
EFFECTPLOT statement, 422
GENMOD procedure, 422
LOGISTIC procedure, 422
ORTHOREG procedure, 422
PLM procedure, 422
SLICE statement (GLIMMIX), 468
SLICE statement (MIXED), 468
optimization technique
GLIMMIX procedure, 492
options summary
CODE statement (GENMOD), 391
CODE statement (GLIMMIX), 391
CODE statement (GLM), 391
CODE statement (GLMSELECT), 391
CODE statement (LOGISTIC), 391
CODE statement (MIXED), 391
CODE statement (PLM), 391
CODE statement (REG), 391
EFFECT statement, 394
ESTIMATE statement, 439
ESTIMATE statement (LIFEREG), 439
ESTIMATE statement (LOGISTIC), 439
ESTIMATE statement (ORTHOREG), 439
ESTIMATE statement (PHREG), 439
ESTIMATE statement (PLM), 439
ESTIMATE statement (PROBIT), 439
ESTIMATE statement (QUANTREG), 439
ESTIMATE statement (SURVEYLOGISTIC),
439
ESTIMATE statement (SURVEYPHREG), 439
ESTIMATE statement (SURVEYREG), 439
LSMEANS statement (GENMOD), 454
LSMEANS statement (LIFEREG), 454
LSMEANS statement (LOGISTIC), 454
LSMEANS statement (ORTHOREG), 454
LSMEANS statement (PHREG), 454
LSMEANS statement (PLM), 454
LSMEANS statement (PROBIT), 454
LSMEANS statement (SURVEYLOGISTIC),
454
LSMEANS statement (SURVEYPHREG), 454
LSMEANS statement (SURVEYREG), 454
LSMESTIMATE statement (GENMOD), 471
LSMESTIMATE statement (LIFEREG), 471
LSMESTIMATE statement (LOGISTIC), 471
LSMESTIMATE statement (MIXED), 471
LSMESTIMATE statement (ORTHOREG), 471
LSMESTIMATE statement (PHREG), 471
LSMESTIMATE statement (PLM), 471
LSMESTIMATE statement (PROBIT), 471
LSMESTIMATE statement
(SURVEYLOGISTIC), 471
LSMESTIMATE statement (SURVEYPHREG),
471
LSMESTIMATE statement (SURVEYREG),
471
NLOPTIONS statement (CALIS), 482
NLOPTIONS statement (GLIMMIX), 482
NLOPTIONS statement (HPMIXED), 482
NLOPTIONS statement (PHREG), 482
NLOPTIONS statement (SURVEYPHREG), 482
NLOPTIONS statement (VARIOGRAM), 482
SLICE statement (GENMOD), 454
SLICE statement (GLIMMIX), 454
SLICE statement (LIFEREG), 454
SLICE statement (LOGISTIC), 454
SLICE statement (MIXED), 454
SLICE statement (ORTHOREG), 454
SLICE statement (PHREG), 454
SLICE statement (PLM), 454
SLICE statement (PROBIT), 454
SLICE statement (SURVEYLOGISTIC), 454
SLICE statement (SURVEYPHREG), 454
SLICE statement (SURVEYREG), 454
TEST statement (LIFEREG), 503
TEST statement (ORTHOREG), 503
TEST statement (PLM), 503
TEST statement (PROBIT), 503
TEST statement (SURVEYPHREG), 503
TEST statement (SURVEYREG), 503
ordering
of class levels (Shared Concepts), 381
ordinal parameterization
Shared Concepts, 388
ortheffect parameterization
Shared Concepts, 389
orthordinal parameterization
Shared Concepts, 389
ORTHOREG procedure
analysis of means, 461
B-spline basis, 408
chi-bar-square statistic, 451
collection effect, 395
diffogram, 464
joint hypothesis tests with complex alternatives,
451
lag effect, 395
multimember effect, 398
Natural cubic spline basis, 411
observed margins, 462
ODS graph names, 422
polynomial effect, 399
positional and nonpositional syntax, 448
spline bases, 406
spline effect, 403
TPF basis, 407
truncated power function basis, 407
ORTHOREG procedure, ESTIMATE statement
ODS table names, 452
ORTHOREG procedure, LSMEANS statement
ODS graph names, 468
ODS table names, 468
orthoterm parameterization
Shared Concepts, 389
orthpoly parameterization
Shared Concepts, 390
orthref parameterization
Shared Concepts, 390
parameterization
effect (Shared Concepts), 387
GLM (Shared Concepts), 388
ordinal (Shared Concepts), 388
ortheffect (Shared Concepts), 389
orthordinal (Shared Concepts), 389
orthoterm (Shared Concepts), 389
orthpoly (Shared Concepts), 390
orthref (Shared Concepts), 390
polynomial (Shared Concepts), 388
reference (Shared Concepts), 389
Shared Concepts, 383
thermometer (Shared Concepts), 388
PHREG procedure
analysis of means, 461
B-spline basis, 408
chi-bar-square statistic, 451
collection effect, 395
diffogram, 464
joint hypothesis tests with complex alternatives,
451
lag effect, 395
multimember effect, 398
Natural cubic spline basis, 411
observed margins, 462
polynomial effect, 399
positional and nonpositional syntax, 448
spline bases, 406
spline effect, 403
TPF basis, 407
truncated power function basis, 407
PHREG procedure, ESTIMATE statement
ODS graph names, 452
ODS table names, 452
PHREG procedure, LSMEANS statement
ODS graph names, 468
ODS table names, 468
PLM procedure
analysis of means, 461
chi-bar-square statistic, 451
diffogram, 464
joint hypothesis tests with complex alternatives,
451
observed margins, 462
ODS graph names, 422
positional and nonpositional syntax, 448
PLM procedure, ESTIMATE statement
ODS graph names, 452
ODS table names, 452
PLM procedure, LSMEANS statement
ODS graph names, 468
ODS table names, 468
PLS procedure
B-spline basis, 408
collection effect, 395
lag effect, 395
multimember effect, 398
Natural cubic spline basis, 411
polynomial effect, 399
spline bases, 406
spline effect, 403
TPF basis, 407
truncated power function basis, 407
polynomial effect
GLIMMIX procedure, 399
GLMSELECT procedure, 399
HPMIXED procedure, 399
LOGISTIC procedure, 399
ORTHOREG procedure, 399
PHREG procedure, 399
PLS procedure, 399
QUANTLIFE procedure, 399
QUANTREG procedure, 399
QUANTSELECT procedure, 399
ROBUSTREG procedure, 399
SURVEYLOGISTIC procedure, 399
SURVEYREG procedure, 399
polynomial effects
Shared Concepts, 383
polynomial parameterization
Shared Concepts, 388
PROBIT procedure
analysis of means, 461
chi-bar-square statistic, 451
diffogram, 464
joint hypothesis tests with complex alternatives,
451
observed margins, 462
positional and nonpositional syntax, 448
PROBIT procedure, ESTIMATE statement
ODS table names, 452
PROBIT procedure, LSMEANS statement
ODS graph names, 468
ODS table names, 468
programming statements
Shared Concepts, 504
QUANTLIFE procedure
B-spline basis, 408
collection effect, 395
lag effect, 395
multimember effect, 398
Natural cubic spline basis, 411
polynomial effect, 399
spline bases, 406
spline effect, 403
TPF basis, 407
truncated power function basis, 407
QUANTREG procedure
B-spline basis, 408
chi-bar-square statistic, 451
collection effect, 395
joint hypothesis tests with complex alternatives,
451
lag effect, 395
multimember effect, 398
Natural cubic spline basis, 411
polynomial effect, 399
positional and nonpositional syntax, 448
spline bases, 406
spline effect, 403
TPF basis, 407
truncated power function basis, 407
QUANTREG procedure, ESTIMATE statement
ODS table names, 452
QUANTSELECT procedure
B-spline basis, 408
collection effect, 395
lag effect, 395
multimember effect, 398
Natural cubic spline basis, 411
polynomial effect, 399
spline bases, 406
spline effect, 403
TPF basis, 407
truncated power function basis, 407
quasi-Newton method
Shared Concepts, 496
reference parameterization
Shared Concepts, 389
regression effects
Shared Concepts, 383
remote monitoring
GLIMMIX procedure, 492
ROBUSTREG procedure
B-spline basis, 408
collection effect, 395
lag effect, 395
multimember effect, 398
Natural cubic spline basis, 411
polynomial effect, 399
spline bases, 406
spline effect, 403
TPF basis, 407
truncated power function basis, 407
second-order algorithm
Shared Concepts, 494
Shared Concepts
bar (|) operator, 383
choosing optimization algorithm, 494
CLASS statement, 380
classification variables, 380
CODE statement, 391
collection effect (EFFECT statement), 395
conjugate gradient method, 498
continuous-by-class effects, 386
continuous-nesting-class effects, 385
crossed effects, 384
double-dogleg method, 497
effect parameterization, 387
EFFECT statement, 393
EFFECTPLOT statement, 411
ESTIMATE statement, 438
first-order algorithm, 494
general effects, 386
GLM parameterization, 388
interaction effects, 384
intercept, 383
lag effect (EFFECT statement), 395
levelization, 380
LSMEANS statement, 454
LSMESTIMATE statement, 471
main effects, 384
missing values, class variables, 382
multimember effect (EFFECT statement), 398
Nelder-Mead simplex method, 498
nested effects, 385
nested versus crossed effects, 385
Newton-Raphson method, 496
Newton-Raphson with ridging, 496
NLOPTIONS statement, 482
ORDER= option, 381
ordering of class levels, 381
ordinal parameterization, 388
ortheffect parameterization, 389
orthordinal parameterization, 389
orthoterm parameterization, 389
orthpoly parameterization, 390
orthref parameterization, 390
parameterization, 383
polynomial effect (EFFECT statement), 399
polynomial effects, 383
polynomial parameterization, 388
programming statements, 504
quasi-Newton method, 496
reference parameterization, 389
regression effects, 383
second-order algorithm, 494
simplex method, 498
singular parameterization, 384
SLICE statement, 500
sort order of class levels, 381
spline bases, 406
spline basis, B-spline, 408
spline basis, Natural cubic spline, 411
spline basis, truncated power function, 407
spline effect (EFFECT statement), 403
splines, 406
TEST statement, 503
thermometer parameterization, 388
trust region method, 495
simplex method
Shared Concepts, 498
singular parameterization
Shared Concepts, 384
SLICE statement
syntax (Shared Concepts), 500
sort order
of class levels (Shared Concepts), 381
spline bases
GLIMMIX procedure, 406
GLMSELECT procedure, 406
HPMIXED procedure, 406
LOGISTIC procedure, 406
ORTHOREG procedure, 406
PHREG procedure, 406
PLS procedure, 406
QUANTLIFE procedure, 406
QUANTREG procedure, 406
QUANTSELECT procedure, 406
ROBUSTREG procedure, 406
Shared Concepts, 406
SURVEYLOGISTIC procedure, 406
SURVEYREG procedure, 406
spline effect
GLIMMIX procedure, 403
GLMSELECT procedure, 403
HPMIXED procedure, 403
LOGISTIC procedure, 403
ORTHOREG procedure, 403
PHREG procedure, 403
PLS procedure, 403
QUANTLIFE procedure, 403
QUANTREG procedure, 403
QUANTSELECT procedure, 403
ROBUSTREG procedure, 403
SURVEYLOGISTIC procedure, 403
SURVEYREG procedure, 403
splines
Shared Concepts, 406
SURVEYLOGISTIC procedure
analysis of means, 461
B-spline basis, 408
chi-bar-square statistic, 451
collection effect, 395
diffogram, 464
joint hypothesis tests with complex alternatives,
451
lag effect, 395
multimember effect, 398
Natural cubic spline basis, 411
observed margins, 462
polynomial effect, 399
positional and nonpositional syntax, 448
spline bases, 406
spline effect, 403
TPF basis, 407
truncated power function basis, 407
SURVEYLOGISTIC procedure, ESTIMATE
statement
ODS table names, 452
SURVEYLOGISTIC procedure, LSMEANS
statement
ODS graph names, 468
ODS table names, 468
SURVEYPHREG procedure
analysis of means, 461
chi-bar-square statistic, 451
diffogram, 464
joint hypothesis tests with complex alternatives,
451
observed margins, 462
positional and nonpositional syntax, 448
SURVEYPHREG procedure, ESTIMATE statement
ODS table names, 452
SURVEYPHREG procedure, LSMEANS statement
ODS graph names, 468
ODS table names, 468
SURVEYREG procedure
analysis of means, 461
B-spline basis, 408
chi-bar-square statistic, 451
collection effect, 395
diffogram, 464
joint hypothesis tests with complex alternatives,
451
lag effect, 395
multimember effect, 398
Natural cubic spline basis, 411
observed margins, 462
polynomial effect, 399
positional and nonpositional syntax, 448
spline bases, 406
spline effect, 403
TPF basis, 407
truncated power function basis, 407
SURVEYREG procedure, ESTIMATE statement
ODS table names, 452
SURVEYREG procedure, LSMEANS statement
ODS graph names, 468
ODS table names, 468
TEST statement
syntax (Shared Concepts), 503
thermometer parameterization
Shared Concepts, 388
TPF basis
GLIMMIX procedure, 407
GLMSELECT procedure, 407
HPMIXED procedure, 407
LOGISTIC procedure, 407
ORTHOREG procedure, 407
PHREG procedure, 407
PLS procedure, 407
QUANTLIFE procedure, 407
QUANTREG procedure, 407
QUANTSELECT procedure, 407
ROBUSTREG procedure, 407
SURVEYLOGISTIC procedure, 407
SURVEYREG procedure, 407
truncated power function
spline basis (Shared Concepts), 407
truncated power function basis
GLIMMIX procedure, 407
GLMSELECT procedure, 407
HPMIXED procedure, 407
LOGISTIC procedure, 407
ORTHOREG procedure, 407
PHREG procedure, 407
PLS procedure, 407
QUANTLIFE procedure, 407
QUANTREG procedure, 407
QUANTSELECT procedure, 407
ROBUSTREG procedure, 407
SURVEYLOGISTIC procedure, 407
SURVEYREG procedure, 407
trust region method
Shared Concepts, 495
Syntax Index
ABSCONV option
NLOPTIONS statement (CALIS), 484
NLOPTIONS statement (GLIMMIX), 484
NLOPTIONS statement (HPMIXED), 484
NLOPTIONS statement (PHREG), 484
NLOPTIONS statement (SURVEYPHREG), 484
NLOPTIONS statement (VARIOGRAM), 484
ABSFCONV option
NLOPTIONS statement (CALIS), 484
NLOPTIONS statement (GLIMMIX), 484
NLOPTIONS statement (HPMIXED), 484
NLOPTIONS statement (PHREG), 484
NLOPTIONS statement (SURVEYPHREG), 484
NLOPTIONS statement (VARIOGRAM), 484
ABSGCONV option
NLOPTIONS statement (CALIS), 484
NLOPTIONS statement (GLIMMIX), 484
NLOPTIONS statement (HPMIXED), 484
NLOPTIONS statement (PHREG), 484
NLOPTIONS statement (SURVEYPHREG), 484
NLOPTIONS statement (VARIOGRAM), 484
ABSGTOL option
NLOPTIONS statement (CALIS), 484
NLOPTIONS statement (GLIMMIX), 484
NLOPTIONS statement (HPMIXED), 484
NLOPTIONS statement (PHREG), 484
NLOPTIONS statement (SURVEYPHREG), 484
NLOPTIONS statement (VARIOGRAM), 484
ABSTOL option
NLOPTIONS statement (CALIS), 484
NLOPTIONS statement (GLIMMIX), 484
NLOPTIONS statement (HPMIXED), 484
NLOPTIONS statement (PHREG), 484
NLOPTIONS statement (SURVEYPHREG), 484
NLOPTIONS statement (VARIOGRAM), 484
ABSXCONV option
NLOPTIONS statement (CALIS), 484
NLOPTIONS statement (GLIMMIX), 484
NLOPTIONS statement (HPMIXED), 484
NLOPTIONS statement (PHREG), 484
NLOPTIONS statement (SURVEYPHREG), 484
NLOPTIONS statement (VARIOGRAM), 484
ABSXTOL option
NLOPTIONS statement (CALIS), 484
NLOPTIONS statement (GLIMMIX), 484
NLOPTIONS statement (HPMIXED), 484
NLOPTIONS statement (PHREG), 484
NLOPTIONS statement (SURVEYPHREG), 484
NLOPTIONS statement (VARIOGRAM), 484
ADJDFE= option
ESTIMATE statement (ORTHOREG), 440
ESTIMATE statement (PLM), 440
ESTIMATE statement (SURVEYPHREG), 440
ESTIMATE statement (SURVEYREG), 440
LSMEANS statement (ORTHOREG), 455
LSMEANS statement (PLM), 455
LSMEANS statement (SURVEYPHREG), 455
LSMEANS statement (SURVEYREG), 455
LSMESTIMATE statement (MIXED), 472
LSMESTIMATE statement (ORTHOREG), 472
LSMESTIMATE statement (PLM), 472
LSMESTIMATE statement (SURVEYPHREG),
472
LSMESTIMATE statement (SURVEYREG),
472
SLICE statement (GLIMMIX), 455
SLICE statement (MIXED), 455
SLICE statement (ORTHOREG), 455
SLICE statement (PLM), 455
ADJUST= option
ESTIMATE statement (LIFEREG), 440
ESTIMATE statement (LOGISTIC), 440
ESTIMATE statement (ORTHOREG), 440
ESTIMATE statement (PHREG), 440
ESTIMATE statement (PLM), 440
ESTIMATE statement (PROBIT), 440
ESTIMATE statement (QUANTREG), 440
ESTIMATE statement (SURVEYLOGISTIC),
440
ESTIMATE statement (SURVEYPHREG), 440
ESTIMATE statement (SURVEYREG), 440
LSMEANS statement (GENMOD), 456
LSMEANS statement (LIFEREG), 456
LSMEANS statement (LOGISTIC), 456
LSMEANS statement (ORTHOREG), 456
LSMEANS statement (PHREG), 456
LSMEANS statement (PLM), 456
LSMEANS statement (PROBIT), 456
LSMEANS statement (SURVEYLOGISTIC),
456
LSMEANS statement (SURVEYPHREG), 456
LSMEANS statement (SURVEYREG), 456
LSMESTIMATE statement (GENMOD), 473
LSMESTIMATE statement (LIFEREG), 473
LSMESTIMATE statement (LOGISTIC), 473
LSMESTIMATE statement (MIXED), 473
LSMESTIMATE statement (ORTHOREG), 473
LSMESTIMATE statement (PHREG), 473
LSMESTIMATE statement (PLM), 473
LSMESTIMATE statement (PROBIT), 473
LSMESTIMATE statement
(SURVEYLOGISTIC), 473
LSMESTIMATE statement (SURVEYPHREG),
473
LSMESTIMATE statement (SURVEYREG),
473
SLICE statement (GENMOD), 456
SLICE statement (GLIMMIX), 456
SLICE statement (LIFEREG), 456
SLICE statement (LOGISTIC), 456
SLICE statement (MIXED), 456
SLICE statement (ORTHOREG), 456
SLICE statement (PHREG), 456
SLICE statement (PLM), 456
SLICE statement (PROBIT), 456
SLICE statement (SURVEYLOGISTIC), 456
SLICE statement (SURVEYPHREG), 456
SLICE statement (SURVEYREG), 456
ALPHA= option
EFFECTPLOT statement, 414
ESTIMATE statement (LIFEREG), 441
ESTIMATE statement (LOGISTIC), 441
ESTIMATE statement (ORTHOREG), 441
ESTIMATE statement (PHREG), 441
ESTIMATE statement (PLM), 441
ESTIMATE statement (PROBIT), 441
ESTIMATE statement (QUANTREG), 441
ESTIMATE statement (SURVEYLOGISTIC),
441
ESTIMATE statement (SURVEYPHREG), 441
ESTIMATE statement (SURVEYREG), 441
LSMEANS statement (GENMOD), 458
LSMEANS statement (LIFEREG), 458
LSMEANS statement (LOGISTIC), 458
LSMEANS statement (ORTHOREG), 458
LSMEANS statement (PHREG), 458
LSMEANS statement (PLM), 458
LSMEANS statement (PROBIT), 458
LSMEANS statement (SURVEYLOGISTIC),
458
LSMEANS statement (SURVEYPHREG), 458
LSMEANS statement (SURVEYREG), 458
LSMESTIMATE statement (GENMOD), 473
LSMESTIMATE statement (LIFEREG), 473
LSMESTIMATE statement (LOGISTIC), 473
LSMESTIMATE statement (MIXED), 473
LSMESTIMATE statement (ORTHOREG), 473
LSMESTIMATE statement (PHREG), 473
LSMESTIMATE statement (PLM), 473
LSMESTIMATE statement (PROBIT), 473
LSMESTIMATE statement
(SURVEYLOGISTIC), 473
LSMESTIMATE statement (SURVEYPHREG),
473
LSMESTIMATE statement (SURVEYREG),
473
SLICE statement (GENMOD), 458
SLICE statement (GLIMMIX), 458
SLICE statement (LIFEREG), 458
SLICE statement (LOGISTIC), 458
SLICE statement (MIXED), 458
SLICE statement (ORTHOREG), 458
SLICE statement (PHREG), 458
SLICE statement (PLM), 458
SLICE statement (PROBIT), 458
SLICE statement (SURVEYLOGISTIC), 458
SLICE statement (SURVEYPHREG), 458
SLICE statement (SURVEYREG), 458
ASINGULAR= option
NLOPTIONS statement (CALIS), 485
NLOPTIONS statement (GLIMMIX), 485
NLOPTIONS statement (HPMIXED), 485
NLOPTIONS statement (PHREG), 485
NLOPTIONS statement (SURVEYPHREG), 485
NLOPTIONS statement (VARIOGRAM), 485
AT option
EFFECTPLOT statement, 414
AT= option
LSMEANS statement (GENMOD), 458
LSMEANS statement (LIFEREG), 458
LSMEANS statement (LOGISTIC), 458
LSMEANS statement (ORTHOREG), 458
LSMEANS statement (PHREG), 458
LSMEANS statement (PLM), 458
LSMEANS statement (PROBIT), 458
LSMEANS statement (SURVEYLOGISTIC),
458
LSMEANS statement (SURVEYPHREG), 458
LSMEANS statement (SURVEYREG), 458
LSMESTIMATE statement (GENMOD), 473
LSMESTIMATE statement (LIFEREG), 473
LSMESTIMATE statement (LOGISTIC), 473
LSMESTIMATE statement (MIXED), 473
LSMESTIMATE statement (ORTHOREG), 473
LSMESTIMATE statement (PHREG), 473
LSMESTIMATE statement (PLM), 473
LSMESTIMATE statement (PROBIT), 473
LSMESTIMATE statement
(SURVEYLOGISTIC), 473
LSMESTIMATE statement (SURVEYPHREG),
473
LSMESTIMATE statement (SURVEYREG),
473
SLICE statement (GENMOD), 458
SLICE statement (GLIMMIX), 458
SLICE statement (LIFEREG), 458
SLICE statement (LOGISTIC), 458
SLICE statement (MIXED), 458
SLICE statement (ORTHOREG), 458
SLICE statement (PHREG), 458
SLICE statement (PLM), 458
SLICE statement (PROBIT), 458
SLICE statement (SURVEYLOGISTIC), 458
SLICE statement (SURVEYPHREG), 458
SLICE statement (SURVEYREG), 458
ATLEN= option
EFFECTPLOT statement, 415
ATORDER= option
EFFECTPLOT statement, 415
BASIS option
EFFECT statement, spline (GLIMMIX), 403
EFFECT statement, spline (GLMSELECT), 403
EFFECT statement, spline (HPMIXED), 403
EFFECT statement, spline (LOGISTIC), 403
EFFECT statement, spline (ORTHOREG), 403
EFFECT statement, spline (PHREG), 403
EFFECT statement, spline (PLS), 403
EFFECT statement, spline (QUANTLIFE), 403
EFFECT statement, spline (QUANTREG), 403
EFFECT statement, spline (QUANTSELECT),
403
EFFECT statement, spline (ROBUSTREG), 403
EFFECT statement, spline
(SURVEYLOGISTIC), 403
EFFECT statement, spline (SURVEYREG), 403
BYLEVEL option
LSMEANS statement (GENMOD), 459
LSMEANS statement (LIFEREG), 459
LSMEANS statement (LOGISTIC), 459
LSMEANS statement (ORTHOREG), 459
LSMEANS statement (PHREG), 459
LSMEANS statement (PLM), 459
LSMEANS statement (PROBIT), 459
LSMEANS statement (SURVEYLOGISTIC),
459
LSMEANS statement (SURVEYPHREG), 459
LSMEANS statement (SURVEYREG), 459
LSMESTIMATE statement (GENMOD), 473
LSMESTIMATE statement (LIFEREG), 473
LSMESTIMATE statement (LOGISTIC), 473
LSMESTIMATE statement (MIXED), 473
LSMESTIMATE statement (ORTHOREG), 473
LSMESTIMATE statement (PHREG), 473
LSMESTIMATE statement (PLM), 473
LSMESTIMATE statement (PROBIT), 473
LSMESTIMATE statement
(SURVEYLOGISTIC), 473
LSMESTIMATE statement (SURVEYPHREG),
473
LSMESTIMATE statement (SURVEYREG),
473
SLICE statement (GENMOD), 459
SLICE statement (GLIMMIX), 459
SLICE statement (LIFEREG), 459
SLICE statement (LOGISTIC), 459
SLICE statement (MIXED), 459
SLICE statement (ORTHOREG), 459
SLICE statement (PHREG), 459
SLICE statement (PLM), 459
SLICE statement (PROBIT), 459
SLICE statement (SURVEYLOGISTIC), 459
SLICE statement (SURVEYPHREG), 459
SLICE statement (SURVEYREG), 459
CALIS procedure, NLOPTIONS statement
ABSCONV option, 484
ABSFCONV option, 484
ABSGCONV option, 484
ABSGTOL option, 484
ABSTOL option, 484
ABSXCONV option, 484
ABSXTOL option, 484
ASINGULAR= option, 485
FCONV option, 485
FCONV2 option, 486
FSIZE option, 486
FTOL option, 485
FTOL2 option, 486
GCONV option, 486
GCONV2 option, 487
GTOL option, 486
GTOL2 option, 487
HESCAL option, 487
HS option, 487
INHESSIAN option, 488
INSTEP option, 488
LCDEACT= option, 488
LCEPSILON= option, 489
LCSINGULAR= option, 489
LINESEARCH option, 489
LIS option, 489
LSPRECISION option, 490
MAXFU option, 490
MAXFUNC option, 490
MAXIT option, 490
MAXITER option, 490
MAXSTEP option, 491
MAXTIME option, 491
MINIT option, 491
MINITER option, 491
MSINGULAR= option, 491
REST option, 491
RESTART option, 491
SINGULAR= option, 492
SOCKET option, 492
TECH option, 492
TECHNIQUE option, 492
UPD option, 493
VSINGULAR= option, 494
XSIZE option, 494
XTOL option, 494
CATALOG= option
CODE statement (GENMOD), 391
CODE statement (GLIMMIX), 391
CODE statement (GLM), 391
CODE statement (GLMSELECT), 391
CODE statement (LOGISTIC), 391
CODE statement (MIXED), 391
CODE statement (PLM), 391
CODE statement (REG), 391
CATEGORY= option
ESTIMATE statement (LOGISTIC), 441
ESTIMATE statement (PLM), 441
ESTIMATE statement (PROBIT), 441
ESTIMATE statement (SURVEYLOGISTIC),
441
LSMESTIMATE statement (GENMOD), 473
LSMESTIMATE statement (LIFEREG), 473
LSMESTIMATE statement (LOGISTIC), 473
LSMESTIMATE statement (PLM), 473
LSMESTIMATE statement (PROBIT), 473
LSMESTIMATE statement
(SURVEYLOGISTIC), 473
CHISQ option
ESTIMATE statement (ORTHOREG), 442
ESTIMATE statement (PLM), 442
ESTIMATE statement (SURVEYPHREG), 442
ESTIMATE statement (SURVEYREG), 442
LSMESTIMATE statement (MIXED), 474
LSMESTIMATE statement (ORTHOREG), 474
LSMESTIMATE statement (PLM), 474
LSMESTIMATE statement (SURVEYPHREG),
474
LSMESTIMATE statement (SURVEYREG),
474
TEST statement (LIFEREG), 503
TEST statement (ORTHOREG), 503
TEST statement (PLM), 503
TEST statement (PROBIT), 503
TEST statement (SURVEYPHREG), 503
TEST statement (SURVEYREG), 503
CL option
ESTIMATE statement (LIFEREG), 442
ESTIMATE statement (LOGISTIC), 442
ESTIMATE statement (ORTHOREG), 442
ESTIMATE statement (PHREG), 442
ESTIMATE statement (PLM), 442
ESTIMATE statement (PROBIT), 442
ESTIMATE statement (QUANTREG), 442
ESTIMATE statement (SURVEYLOGISTIC),
442
ESTIMATE statement (SURVEYPHREG), 442
ESTIMATE statement (SURVEYREG), 442
LSMEANS statement (GENMOD), 459
LSMEANS statement (LIFEREG), 459
LSMEANS statement (LOGISTIC), 459
LSMEANS statement (ORTHOREG), 459
LSMEANS statement (PHREG), 459
LSMEANS statement (PLM), 459
LSMEANS statement (PROBIT), 459
LSMEANS statement (SURVEYLOGISTIC),
459
LSMEANS statement (SURVEYPHREG), 459
LSMEANS statement (SURVEYREG), 459
LSMESTIMATE statement (GENMOD), 474
LSMESTIMATE statement (LIFEREG), 474
LSMESTIMATE statement (LOGISTIC), 474
LSMESTIMATE statement (MIXED), 474
LSMESTIMATE statement (ORTHOREG), 474
LSMESTIMATE statement (PHREG), 474
LSMESTIMATE statement (PLM), 474
LSMESTIMATE statement (PROBIT), 474
LSMESTIMATE statement
(SURVEYLOGISTIC), 474
LSMESTIMATE statement (SURVEYPHREG),
474
LSMESTIMATE statement (SURVEYREG),
474
SLICE statement (GENMOD), 459
SLICE statement (GLIMMIX), 459
SLICE statement (LIFEREG), 459
SLICE statement (LOGISTIC), 459
SLICE statement (MIXED), 459
SLICE statement (ORTHOREG), 459
SLICE statement (PHREG), 459
SLICE statement (PLM), 459
SLICE statement (PROBIT), 459
SLICE statement (SURVEYLOGISTIC), 459
SLICE statement (SURVEYPHREG), 459
SLICE statement (SURVEYREG), 459
CLI option
EFFECTPLOT statement, 415
CLM option
EFFECTPLOT statement, 415
CLUSTER option
EFFECTPLOT statement, 415
CODE statement
GENMOD procedure, 390
GLIMMIX procedure, 390
GLM procedure, 390
GLMSELECT procedure, 390
LOGISTIC procedure, 390
MIXED procedure, 390
PLM procedure, 390
REG procedure, 390
CONNECT option
EFFECTPLOT statement, 416
CORR option
ESTIMATE statement (LIFEREG), 442
ESTIMATE statement (LOGISTIC), 442
ESTIMATE statement (ORTHOREG), 442
ESTIMATE statement (PHREG), 442
ESTIMATE statement (PLM), 442
ESTIMATE statement (PROBIT), 442
ESTIMATE statement (QUANTREG), 442
ESTIMATE statement (SURVEYLOGISTIC),
442
ESTIMATE statement (SURVEYPHREG), 442
ESTIMATE statement (SURVEYREG), 442
LSMEANS statement (GENMOD), 459
LSMEANS statement (LIFEREG), 459
LSMEANS statement (LOGISTIC), 459
LSMEANS statement (ORTHOREG), 459
LSMEANS statement (PHREG), 459
LSMEANS statement (PLM), 459
LSMEANS statement (PROBIT), 459
LSMEANS statement (SURVEYLOGISTIC),
459
LSMEANS statement (SURVEYPHREG), 459
LSMEANS statement (SURVEYREG), 459
LSMESTIMATE statement (GENMOD), 474
LSMESTIMATE statement (LIFEREG), 474
LSMESTIMATE statement (LOGISTIC), 474
LSMESTIMATE statement (MIXED), 474
LSMESTIMATE statement (ORTHOREG), 474
LSMESTIMATE statement (PHREG), 474
LSMESTIMATE statement (PLM), 474
LSMESTIMATE statement (PROBIT), 474
LSMESTIMATE statement
(SURVEYLOGISTIC), 474
LSMESTIMATE statement (SURVEYPHREG),
474
LSMESTIMATE statement (SURVEYREG),
474
SLICE statement (GENMOD), 459
SLICE statement (GLIMMIX), 459
SLICE statement (LIFEREG), 459
SLICE statement (LOGISTIC), 459
SLICE statement (MIXED), 459
SLICE statement (ORTHOREG), 459
SLICE statement (PHREG), 459
SLICE statement (PLM), 459
SLICE statement (PROBIT), 459
SLICE statement (SURVEYLOGISTIC), 459
SLICE statement (SURVEYPHREG), 459
SLICE statement (SURVEYREG), 459
COV option
ESTIMATE statement (LIFEREG), 442
ESTIMATE statement (LOGISTIC), 442
ESTIMATE statement (ORTHOREG), 442
ESTIMATE statement (PHREG), 442
ESTIMATE statement (PLM), 442
ESTIMATE statement (PROBIT), 442
ESTIMATE statement (QUANTREG), 442
ESTIMATE statement (SURVEYLOGISTIC),
442
ESTIMATE statement (SURVEYPHREG), 442
ESTIMATE statement (SURVEYREG), 442
LSMEANS statement (GENMOD), 459
LSMEANS statement (LIFEREG), 459
LSMEANS statement (LOGISTIC), 459
LSMEANS statement (ORTHOREG), 459
LSMEANS statement (PHREG), 459
LSMEANS statement (PLM), 459
LSMEANS statement (PROBIT), 459
LSMEANS statement (SURVEYLOGISTIC),
459
LSMEANS statement (SURVEYPHREG), 459
LSMEANS statement (SURVEYREG), 459
LSMESTIMATE statement (GENMOD), 474
LSMESTIMATE statement (LIFEREG), 474
LSMESTIMATE statement (LOGISTIC), 474
LSMESTIMATE statement (MIXED), 474
LSMESTIMATE statement (ORTHOREG), 474
LSMESTIMATE statement (PHREG), 474
LSMESTIMATE statement (PLM), 474
LSMESTIMATE statement (PROBIT), 474
LSMESTIMATE statement
(SURVEYLOGISTIC), 474
LSMESTIMATE statement (SURVEYPHREG),
474
LSMESTIMATE statement (SURVEYREG),
474
SLICE statement (GENMOD), 459
SLICE statement (GLIMMIX), 459
SLICE statement (LIFEREG), 459
SLICE statement (LOGISTIC), 459
SLICE statement (MIXED), 459
SLICE statement (ORTHOREG), 459
SLICE statement (PHREG), 459
SLICE statement (PLM), 459
SLICE statement (PROBIT), 459
SLICE statement (SURVEYLOGISTIC), 459
SLICE statement (SURVEYPHREG), 459
SLICE statement (SURVEYREG), 459
DAMPSTEP option
NLOPTIONS statement (GLIMMIX), 485
DATABOUNDARY option
EFFECT statement, spline (GLIMMIX), 404
EFFECT statement, spline (GLMSELECT), 404
EFFECT statement, spline (HPMIXED), 404
EFFECT statement, spline (LOGISTIC), 404
EFFECT statement, spline (ORTHOREG), 404
EFFECT statement, spline (PHREG), 404
EFFECT statement, spline (PLS), 404
EFFECT statement, spline (QUANTLIFE), 404
EFFECT statement, spline (QUANTREG), 404
EFFECT statement, spline (QUANTSELECT),
404
EFFECT statement, spline (ROBUSTREG), 404
EFFECT statement, spline
(SURVEYLOGISTIC), 404
EFFECT statement, spline (SURVEYREG), 404
DDF= option
TEST statement (LIFEREG), 503
TEST statement (ORTHOREG), 503
TEST statement (PLM), 503
TEST statement (PROBIT), 503
TEST statement (SURVEYPHREG), 503
TEST statement (SURVEYREG), 503
DEGREE option
EFFECT statement, polynomial (GLIMMIX),
400
EFFECT statement, polynomial
(GLMSELECT), 400
EFFECT statement, polynomial (HPMIXED),
400
EFFECT statement, polynomial (LOGISTIC),
400
EFFECT statement, polynomial (ORTHOREG),
400
EFFECT statement, polynomial (PHREG), 400
EFFECT statement, polynomial (PLS), 400
EFFECT statement, polynomial (QUANTLIFE),
400
EFFECT statement, polynomial (QUANTREG),
400
EFFECT statement, polynomial
(QUANTSELECT), 400
EFFECT statement, polynomial
(ROBUSTREG), 400
EFFECT statement, polynomial
(SURVEYLOGISTIC), 400
EFFECT statement, polynomial
(SURVEYREG), 400
EFFECT statement, spline (GLIMMIX), 404
EFFECT statement, spline (GLMSELECT), 404
EFFECT statement, spline (HPMIXED), 404
EFFECT statement, spline (LOGISTIC), 404
EFFECT statement, spline (ORTHOREG), 404
EFFECT statement, spline (PHREG), 404
EFFECT statement, spline (PLS), 404
EFFECT statement, spline (QUANTLIFE), 404
EFFECT statement, spline (QUANTREG), 404
EFFECT statement, spline (QUANTSELECT),
404
EFFECT statement, spline (ROBUSTREG), 404
EFFECT statement, spline
(SURVEYLOGISTIC), 404
EFFECT statement, spline (SURVEYREG), 404
DESIGNROLE option
EFFECT statement, lag (GLIMMIX), 397
EFFECT statement, lag (GLMSELECT), 397
EFFECT statement, lag (HPMIXED), 397
EFFECT statement, lag (LOGISTIC), 397
EFFECT statement, lag (ORTHOREG), 397
EFFECT statement, lag (PHREG), 397
EFFECT statement, lag (PLS), 397
EFFECT statement, lag (QUANTLIFE), 397
EFFECT statement, lag (QUANTREG), 397
EFFECT statement, lag (QUANTSELECT), 397
EFFECT statement, lag (ROBUSTREG), 397
EFFECT statement, lag (SURVEYLOGISTIC),
397
EFFECT statement, lag (SURVEYREG), 397
DETAILS option
EFFECT statement, lag (GLIMMIX), 397
EFFECT statement, lag (GLMSELECT), 397
EFFECT statement, lag (HPMIXED), 397
EFFECT statement, lag (LOGISTIC), 397
EFFECT statement, lag (ORTHOREG), 397
EFFECT statement, lag (PHREG), 397
EFFECT statement, lag (PLS), 397
EFFECT statement, lag (QUANTLIFE), 397
EFFECT statement, lag (QUANTREG), 397
EFFECT statement, lag (QUANTSELECT), 397
EFFECT statement, lag (ROBUSTREG), 397
EFFECT statement, lag (SURVEYLOGISTIC),
397
EFFECT statement, lag (SURVEYREG), 397
EFFECT statement, multimember (GLIMMIX),
399
EFFECT statement, multimember
(GLMSELECT), 399
EFFECT statement, multimember (HPMIXED),
399
EFFECT statement, multimember (LOGISTIC),
399
EFFECT statement, multimember
(ORTHOREG), 399
EFFECT statement, multimember (PHREG), 399
EFFECT statement, multimember (PLS), 399
EFFECT statement, multimember
(QUANTLIFE), 399
EFFECT statement, multimember
(QUANTREG), 399
EFFECT statement, multimember
(QUANTSELECT), 399
EFFECT statement, multimember
(ROBUSTREG), 399
EFFECT statement, multimember
(SURVEYLOGISTIC), 399
EFFECT statement, multimember
(SURVEYREG), 399
EFFECT statement, polynomial (GLIMMIX),
400
EFFECT statement, polynomial
(GLMSELECT), 400
EFFECT statement, polynomial (HPMIXED),
400
EFFECT statement, polynomial (LOGISTIC),
400
EFFECT statement, polynomial (ORTHOREG),
400
EFFECT statement, polynomial (PHREG), 400
EFFECT statement, polynomial (PLS), 400
EFFECT statement, polynomial (QUANTLIFE),
400
EFFECT statement, polynomial (QUANTREG),
400
EFFECT statement, polynomial
(QUANTSELECT), 400
EFFECT statement, polynomial
(ROBUSTREG), 400
EFFECT statement, polynomial
(SURVEYLOGISTIC), 400
EFFECT statement, polynomial
(SURVEYREG), 400
EFFECT statement, spline (GLIMMIX), 404
EFFECT statement, spline (GLMSELECT), 404
EFFECT statement, spline (HPMIXED), 404
EFFECT statement, spline (LOGISTIC), 404
EFFECT statement, spline (ORTHOREG), 404
EFFECT statement, spline (PHREG), 404
EFFECT statement, spline (PLS), 404
EFFECT statement, spline (QUANTLIFE), 404
EFFECT statement, spline (QUANTREG), 404
EFFECT statement, spline (QUANTSELECT),
404
EFFECT statement, spline (ROBUSTREG), 404
EFFECT statement, spline
(SURVEYLOGISTIC), 404
EFFECT statement, spline (SURVEYREG), 404
DF= option
ESTIMATE statement (ORTHOREG), 442
ESTIMATE statement (PLM), 442
ESTIMATE statement (SURVEYPHREG), 442
ESTIMATE statement (SURVEYREG), 442
LSMEANS statement (ORTHOREG), 460
LSMEANS statement (PLM), 460
LSMEANS statement (SURVEYPHREG), 460
LSMEANS statement (SURVEYREG), 460
LSMESTIMATE statement (MIXED), 474
LSMESTIMATE statement (ORTHOREG), 474
LSMESTIMATE statement (PLM), 474
LSMESTIMATE statement (SURVEYPHREG),
474
LSMESTIMATE statement (SURVEYREG),
474
SLICE statement (GLIMMIX), 460
SLICE statement (MIXED), 460
SLICE statement (ORTHOREG), 460
SLICE statement (PLM), 460
SLICE statement (SURVEYPHREG), 460
SLICE statement (SURVEYREG), 460
DIFF option
LSMEANS statement (GENMOD), 460
LSMEANS statement (LIFEREG), 460
LSMEANS statement (LOGISTIC), 460
LSMEANS statement (ORTHOREG), 460
LSMEANS statement (PHREG), 460
LSMEANS statement (PLM), 460
LSMEANS statement (PROBIT), 460
LSMEANS statement (SURVEYLOGISTIC),
460
LSMEANS statement (SURVEYPHREG), 460
LSMEANS statement (SURVEYREG), 460
SLICE statement (GENMOD), 460
SLICE statement (GLIMMIX), 460
SLICE statement (LIFEREG), 460
SLICE statement (LOGISTIC), 460
SLICE statement (MIXED), 460
SLICE statement (ORTHOREG), 460
SLICE statement (PHREG), 460
SLICE statement (PLM), 460
SLICE statement (PROBIT), 460
SLICE statement (SURVEYLOGISTIC), 460
SLICE statement (SURVEYPHREG), 460
SLICE statement (SURVEYREG), 460
DIVISOR= option
ESTIMATE statement (LIFEREG), 442
ESTIMATE statement (LOGISTIC), 442
ESTIMATE statement (ORTHOREG), 442
ESTIMATE statement (PHREG), 442
ESTIMATE statement (PLM), 442
ESTIMATE statement (PROBIT), 442
ESTIMATE statement (QUANTREG), 442
ESTIMATE statement (SURVEYLOGISTIC),
442
ESTIMATE statement (SURVEYPHREG), 442
ESTIMATE statement (SURVEYREG), 442
LSMESTIMATE statement (GENMOD), 474
LSMESTIMATE statement (LIFEREG), 474
LSMESTIMATE statement (LOGISTIC), 474
LSMESTIMATE statement (MIXED), 474
LSMESTIMATE statement (ORTHOREG), 474
LSMESTIMATE statement (PHREG), 474
LSMESTIMATE statement (PLM), 474
LSMESTIMATE statement (PROBIT), 474
LSMESTIMATE statement
(SURVEYLOGISTIC), 474
LSMESTIMATE statement (SURVEYPHREG),
474
LSMESTIMATE statement (SURVEYREG),
474
DUMMIES option
CODE statement (GENMOD), 391
CODE statement (GLIMMIX), 391
CODE statement (GLM), 391
CODE statement (GLMSELECT), 391
CODE statement (LOGISTIC), 391
CODE statement (MIXED), 391
CODE statement (PLM), 391
CODE statement (REG), 391
E option
ESTIMATE statement (LIREREG), 443
ESTIMATE statement (LOGISTIC), 443
ESTIMATE statement (ORTHOREG), 443
ESTIMATE statement (PHREG), 443
ESTIMATE statement (PLM), 443
ESTIMATE statement (PROBIT), 443
ESTIMATE statement (QUANTREG), 443
ESTIMATE statement (SURVEYLOGISTIC),
443
ESTIMATE statement (SURVEYPHREG), 443
ESTIMATE statement (SURVEYREG), 443
LSMEANS statement (GENMOD), 461
LSMEANS statement (LIFEREG), 461
LSMEANS statement (LOGISTIC), 461
LSMEANS statement (ORTHOREG), 461
LSMEANS statement (PHREG), 461
LSMEANS statement (PLM), 461
LSMEANS statement (PROBIT), 461
LSMEANS statement (SURVEYLOGISTIC),
461
LSMEANS statement (SURVEYPHREG), 461
LSMEANS statement (SURVEYREG), 461
LSMESTIMATE statement (GENMOD), 475
LSMESTIMATE statement (LIFEREG), 475
LSMESTIMATE statement (LOGISTIC), 475
LSMESTIMATE statement (MIXED), 475
LSMESTIMATE statement (ORTHOREG), 475
LSMESTIMATE statement (PHREG), 475
LSMESTIMATE statement (PLM), 475
LSMESTIMATE statement (PROBIT), 475
LSMESTIMATE statement
(SURVEYLOGISTIC), 475
LSMESTIMATE statement (SURVEYPHREG),
475
LSMESTIMATE statement (SURVEYREG),
475
SLICE statement (GENMOD), 461
SLICE statement (GLIMMIX), 461
SLICE statement (LIFEREG), 461
SLICE statement (LOGISTIC), 461
SLICE statement (MIXED), 461
SLICE statement (ORTHOREG), 461
SLICE statement (PHREG), 461
SLICE statement (PLM), 461
SLICE statement (PROBIT), 461
SLICE statement (SURVEYLOGISTIC), 461
SLICE statement (SURVEYPHREG), 461
SLICE statement (SURVEYREG), 461
TEST statement (LIFEREG), 503
TEST statement (ORTHOREG), 503
TEST statement (PLM), 503
TEST statement (PROBIT), 503
TEST statement (SURVEYPHREG), 503
TEST statement (SURVEYREG), 503
E1 option
TEST statement (LIFEREG), 503
TEST statement (ORTHOREG), 503
TEST statement (PLM), 503
TEST statement (PROBIT), 503
TEST statement (SURVEYPHREG), 503
TEST statement (SURVEYREG), 503
E2 option
TEST statement (LIFEREG), 504
TEST statement (ORTHOREG), 504
TEST statement (PLM), 504
TEST statement (PROBIT), 504
TEST statement (SURVEYPHREG), 504
TEST statement (SURVEYREG), 504
E3 option
TEST statement (LIFEREG), 504
TEST statement (ORTHOREG), 504
TEST statement (PLM), 504
TEST statement (PROBIT), 504
TEST statement (SURVEYPHREG), 504
TEST statement (SURVEYREG), 504
EFFECT statement
collection effect, 395
GLIMMIX procedure, 393
GLMSELECT procedure, 393
HPMIXED procedure, 393
lag effect, 395
LOGISTIC procedure, 393
multimember effect, 398
ORTHOREG procedure, 393
PHREG procedure, 393
PLS procedure, 393
polynomial effect, 399
QUANTLIFE procedure, 393
QUANTREG procedure, 393
QUANTSELECT procedure, 393
ROBUSTREG procedure, 393
spline effect, 403
SURVEYLOGISTIC procedure, 393
SURVEYREG procedure, 393
EFFECTPLOT statement
GENMOD procedure, 412
LOGISTIC procedure, 412
ORTHOREG procedure, 412
PLM procedure, 412
ELSM option
LSMESTIMATE statement (GENMOD), 475
LSMESTIMATE statement (LIFEREG), 475
LSMESTIMATE statement (LOGISTIC), 475
LSMESTIMATE statement (MIXED), 475
LSMESTIMATE statement (ORTHOREG), 475
LSMESTIMATE statement (PHREG), 475
LSMESTIMATE statement (PLM), 475
LSMESTIMATE statement (PROBIT), 475
LSMESTIMATE statement
(SURVEYLOGISTIC), 475
LSMESTIMATE statement (SURVEYPHREG),
475
LSMESTIMATE statement (SURVEYREG),
475
ERRORS option
CODE statement (GENMOD), 392
CODE statement (GLIMMIX), 392
CODE statement (GLM), 392
CODE statement (GLMSELECT), 392
CODE statement (LOGISTIC), 392
CODE statement (MIXED), 392
CODE statement (PLM), 392
CODE statement (REG), 392
ESTIMATE statement
LIFEREG procedure, 437
LOGISTIC procedure, 437
ORTHOREG procedure, 437
PHREG procedure, 437
PLM procedure, 437
PROBIT procedure, 437
QUANTREG procedure, 437
SURVEYLOGISTIC procedure, 437
SURVEYPHREG procedure, 437
SURVEYREG procedure, 437
EXP option
ESTIMATE statement (LIFEREG), 443
ESTIMATE statement (LOGISTIC), 443
ESTIMATE statement (PHREG), 443
ESTIMATE statement (PLM), 443
ESTIMATE statement (PROBIT), 443
ESTIMATE statement (SURVEYLOGISTIC),
443
LSMEANS statement (GENMOD), 461
LSMEANS statement (LIFEREG), 461
LSMEANS statement (LOGISTIC), 461
LSMEANS statement (PHREG), 461
LSMEANS statement (PLM), 461
LSMEANS statement (PROBIT), 461
LSMEANS statement (SURVEYLOGISTIC),
461
LSMESTIMATE statement (GENMOD), 475
LSMESTIMATE statement (LIFEREG), 475
LSMESTIMATE statement (LOGISTIC), 475
LSMESTIMATE statement (PHREG), 475
LSMESTIMATE statement (PLM), 475
LSMESTIMATE statement (PROBIT), 475
LSMESTIMATE statement
(SURVEYLOGISTIC), 475
SLICE statement (GENMOD), 461
SLICE statement (GLIMMIX), 461
SLICE statement (LIFEREG), 461
SLICE statement (LOGISTIC), 461
SLICE statement (PHREG), 461
SLICE statement (PLM), 461
SLICE statement (PROBIT), 461
SLICE statement (SURVEYLOGISTIC), 461
EXTEND= option
EFFECTPLOT statement, 416
FCONV option
NLOPTIONS statement (CALIS), 485
NLOPTIONS statement (GLIMMIX), 485
NLOPTIONS statement (HPMIXED), 485
NLOPTIONS statement (PHREG), 485
NLOPTIONS statement (SURVEYPHREG), 485
NLOPTIONS statement (VARIOGRAM), 485
FCONV2 option
NLOPTIONS statement (CALIS), 486
NLOPTIONS statement (GLIMMIX), 486
NLOPTIONS statement (HPMIXED), 486
NLOPTIONS statement (PHREG), 486
NLOPTIONS statement (SURVEYPHREG), 486
NLOPTIONS statement (VARIOGRAM), 486
FILE= option
CODE statement (GENMOD), 392
CODE statement (GLIMMIX), 392
CODE statement (GLM), 392
CODE statement (GLMSELECT), 392
CODE statement (LOGISTIC), 392
CODE statement (MIXED), 392
CODE statement (PLM), 392
CODE statement (REG), 392
FORMAT= option
CODE statement (GENMOD), 392
CODE statement (GLIMMIX), 392
CODE statement (GLM), 392
CODE statement (GLMSELECT), 392
CODE statement (LOGISTIC), 392
CODE statement (MIXED), 392
CODE statement (PLM), 392
CODE statement (REG), 392
FSIZE option
NLOPTIONS statement (CALIS), 486
NLOPTIONS statement (GLIMMIX), 486
NLOPTIONS statement (HPMIXED), 486
NLOPTIONS statement (PHREG), 486
NLOPTIONS statement (SURVEYPHREG), 486
NLOPTIONS statement (VARIOGRAM), 486
FTOL option
NLOPTIONS statement (CALIS), 485
NLOPTIONS statement (GLIMMIX), 485
NLOPTIONS statement (HPMIXED), 485
NLOPTIONS statement (PHREG), 485
NLOPTIONS statement (SURVEYPHREG), 485
NLOPTIONS statement (VARIOGRAM), 485
FTOL2 option
NLOPTIONS statement (CALIS), 486
NLOPTIONS statement (GLIMMIX), 486
NLOPTIONS statement (HPMIXED), 486
NLOPTIONS statement (PHREG), 486
NLOPTIONS statement (SURVEYPHREG), 486
NLOPTIONS statement (VARIOGRAM), 486
GCONV option
NLOPTIONS statement (CALIS), 486
NLOPTIONS statement (GLIMMIX), 486
NLOPTIONS statement (HPMIXED), 486
NLOPTIONS statement (PHREG), 486
NLOPTIONS statement (SURVEYPHREG), 486
NLOPTIONS statement (VARIOGRAM), 486
GCONV2 option
NLOPTIONS statement (CALIS), 487
NLOPTIONS statement (GLIMMIX), 487
NLOPTIONS statement (HPMIXED), 487
NLOPTIONS statement (PHREG), 487
NLOPTIONS statement (SURVEYPHREG), 487
NLOPTIONS statement (VARIOGRAM), 487
GENMOD procedure, CODE statement
CATALOG= option, 391
DUMMIES option, 391
ERRORS option, 392
FILE= option, 392
FORMAT= option, 392
GROUP= option, 392
IMPUTE option, 392
LINESIZE= option, 392
LOOKUP= option, 392
NODUMMIES option, 391
NOERRORS option, 392
NORESIDUAL option, 393
RESIDUAL option, 393
GENMOD procedure, EFFECTPLOT statement
ALPHA= option, 414
AT option, 414
ATLEN= option, 415
ATORDER= option, 415
CLI option, 415
CLM option, 415
CLUSTER option, 415
CONNECT option, 416
EXTEND= option, 416
GRIDSIZE= option, 416
ILINK option, 416
INDIVIDUAL option, 416
LIMITS option, 416
LINK option, 416
MOFF option, 416
NCOLS= option, 416
NOCLI option, 417
NOCLM option, 417
NOCLUSTER option, 417
NOCONNECT option, 417
NOLIMITS option, 417
NOOBS option, 417
NROWS= option, 417
OBS option, 417
PLOTBY= option, 420
PLOTBYLEN= option, 421
POLYBAR option, 421
PREDLABEL= option, 421
SHOWCLEGEND option, 421
SLICEBY= option, 421
SMOOTH option, 421
UNPACK option, 421
X= option, 421
Y= option, 422
YRANGE= option, 422
GENMOD procedure, LSMEANS statement
ADJUST= option, 456
ALPHA= option, 458
AT= option, 458
BYLEVEL option, 459
CL option, 459
CORR option, 459
COV option, 459
DIFF option, 460
E option, 461
EXP option, 461
ILINK option, 461
LINES option, 461
MEANS or NOMEANS option, 462
OBSMARGINS= option, 462
ODDSRATIO option, 462
ODS graph names, 468
ODS table names, 468
PDIFF option, 463
PLOTS= option, 463
SEED= option, 466
SINGULAR= option, 467
STEPDOWN option, 467
GENMOD procedure, LSMESIIMATE statement
ADJUST= option, 473
ALPHA= option, 473
AT= option, 473
BYLEVEL option, 473
CATEGORY= option, 473
CL option, 474
CORR option, 474
COV option, 474
DIVISOR= option, 474
E option, 475
ELSM option, 475
EXP option, 475
ILINK option, 475
JOINT option, 476
LOWER option, 477
OBSMARGINS= option, 477
ODS graph names, 481
ODS table names, 481
PLOTS= option, 477
SEED= option, 478
SINGULAR= option, 479
STEPDOWN option, 479
TESTVALUE= option, 480
UPPER option, 480
GENMOD procedure, SLICE statement
ADJUST= option, 456
ALPHA= option, 458
AT= option, 458
BYLEVEL option, 459
CL option, 459
CORR option, 459
COV option, 459
DIFF option, 460
E option, 461
EXP option, 461
ILINK option, 461
LINES option, 461
MEANS or NOMEANS option, 462
NOF option, 501
OBSMARGINS= option, 462
ODDSRATIO option, 462
ODS table names, 501
PDIFF option, 463
PLOTS= option, 463
SEED= option, 466
SIMPLE= option, 500
SINGULAR= option, 467
SLICEBY= option, 500
STEPDOWN option, 467
GLIMMIX procedure, CODE statement
CATALOG= option, 391
DUMMIES option, 391
ERRORS option, 392
FILE= option, 392
FORMAT= option, 392
GROUP= option, 392
IMPUTE option, 392
LINESIZE= option, 392
LOOKUP= option, 392
NODUMMIES option, 391
NOERRORS option, 392
NORESIDUAL option, 393
RESIDUAL option, 393
GLIMMIX procedure, EFFECT statement
BASIS option (spline), 403
collection effect, 395
DATABOUNDARY option (spline), 404
DEGREE option (polynomial), 400
DEGREE option (spline), 404
DESIGNROLE option (lag), 397
DETAILS option (lag), 397
DETAILS option (multimember), 399
DETAILS option (polynomial), 400
DETAILS option (spline), 404
KNOTMAX option (spline), 404
KNOTMETHOD option (spline), 404
KNOTMIN option (spline), 406
LABELSTYLE option (polynomial), 400
lag effect, 395
MDEGREE option (polynomial), 401
multimember effect, 398
NATURALCUBIC option (spline), 406
NLAG option (lag), 398
NOEFFECT option (multimember), 399
NOSEPARATE option (polynomial), 401
PERIOD option (lag), 397
polynomial effect, 399
SEPARATE option (spline), 406
spline effect, 403
STANDARDIZE option (polynomial), 401
WITHIN option (lag), 397
GLIMMIX procedure, NLOPTIONS statement
ABSCONV option, 484
ABSFCONV option, 484
ABSGCONV option, 484
ABSGTOL option, 484
ABSTOL option, 484
ABSXCONV option, 484
ABSXTOL option, 484
ASINGULAR= option, 485
DAMPSTEP option, 485
FCONV option, 485
FCONV2 option, 486
FSIZE option, 486
FTOL option, 485
FTOL2 option, 486
GCONV option, 486
GCONV2 option, 487
GTOL option, 486
GTOL2 option, 487
HESCAL option, 487
HS option, 487
INHESS option, 488
INHESSIAN option, 488
INSTEP option, 488
LCDEACT= option, 488
LCEPSILON= option, 489
LCSINGULAR= option, 489
LINESEARCH option, 489
LIS option, 489
LSP option, 490
LSPRECISION option, 490
MAXFU option, 490
MAXFUNC option, 490
MAXIT option, 490
MAXITER option, 490
MAXSTEP option, 491
MAXTIME option, 491
MINIT option, 491
MINITER option, 491
MSINGULAR= option, 491
REST option, 491
RESTART option, 491
SINGULAR= option, 492
SOCKET option, 492
TECH option, 492
TECHNIQUE option, 492
UPD option, 493
UPDATE option, 493
VSINGULAR= option, 494
XCONV option, 494
XSIZE option, 494
XTOL option, 494
GLIMMIX procedure, SLICE statement
ADJDFE= option, 455
ADJUST= option, 456
ALPHA= option, 458
AT= option, 458
BYLEVEL option, 459
CL option, 459
CORR option, 459
COV option, 459
DF= option, 460
DIFF option, 460
E option, 461
EXP option, 461
ILINK option, 461
LINES option, 461
MEANS or NOMEANS option, 462
NOF option, 501
OBSMARGINS= option, 462
ODDSRATIO option, 462
ODS graph names, 468
ODS table names, 501
PDIFF option, 463
PLOTS= option, 463
SEED= option, 466
SIMPLE= option, 500
SINGULAR= option, 467
SLICEBY= option, 500
STEPDOWN option, 467
GLM procedure, CODE statement
CATALOG= option, 391
DUMMIES option, 391
ERRORS option, 392
FILE= option, 392
FORMAT= option, 392
GROUP= option, 392
IMPUTE option, 392
LINESIZE= option, 392
LOOKUP= option, 392
NODUMMIES option, 391
NOERRORS option, 392
NORESIDUAL option, 393
RESIDUAL option, 393
GLMSELECT procedure, CODE statement
CATALOG= option, 391
DUMMIES option, 391
ERRORS option, 392
FILE= option, 392
FORMAT= option, 392
GROUP= option, 392
IMPUTE option, 392
LINESIZE= option, 392
LOOKUP= option, 392
NODUMMIES option, 391
NOERRORS option, 392
NORESIDUAL option, 393
RESIDUAL option, 393
GLMSELECT procedure, EFFECT statement
BASIS option (spline), 403
collection effect, 395
DATABOUNDARY option (spline), 404
DEGREE option (polynomial), 400
DEGREE option (spline), 404
DESIGNROLE option (lag), 397
DETAILS option (lag), 397
DETAILS option (multimember), 399
DETAILS option (polynomial), 400
DETAILS option (spline), 404
KNOTMAX option (spline), 404
KNOTMETHOD option (spline), 404
KNOTMIN option (spline), 406
LABELSTYLE option (polynomial), 400
lag effect, 395
MDEGREE option (polynomial), 401
multimember effect, 398
NATURALCUBIC option (spline), 406
NLAG option (lag), 398
NOEFFECT option (multimember), 399
NOSEPARATE option (polynomial), 401
PERIOD option (lag), 397
polynomial effect, 399
SEPARATE option (spline), 406
spline effect, 403
SPLIT option (spline), 406
STANDARDIZE option (polynomial), 401
WITHIN option (lag), 397
GRIDSIZE= option
EFFECTPLOT statement, 416
GROUP= option
CODE statement (GENMOD), 392
CODE statement (GLIMMIX), 392
CODE statement (GLM), 392
CODE statement (GLMSELECT), 392
CODE statement (LOGISTIC), 392
CODE statement (MIXED), 392
CODE statement (PLM), 392
CODE statement (REG), 392
GTOL option
NLOPTIONS statement (CALIS), 486
NLOPTIONS statement (GLIMMIX), 486
NLOPTIONS statement (HPMIXED), 486
NLOPTIONS statement (PHREG), 486
NLOPTIONS statement (SURVEYPHREG), 486
NLOPTIONS statement (VARIOGRAM), 486
GTOL2 option
NLOPTIONS statement (CALIS), 487
NLOPTIONS statement (GLIMMIX), 487
NLOPTIONS statement (HPMIXED), 487
NLOPTIONS statement (PHREG), 487
NLOPTIONS statement (SURVEYPHREG), 487
NLOPTIONS statement (VARIOGRAM), 487
HESCAL option
NLOPTIONS statement (CALIS), 487
NLOPTIONS statement (GLIMMIX), 487
NLOPTIONS statement (HPMIXED), 487
NLOPTIONS statement (PHREG), 487
NLOPTIONS statement (SURVEYPHREG), 487
NLOPTIONS statement (VARIOGRAM), 487
HPMIXED procedure, EFFECT statement
BASIS option (spline), 403
collection effect, 395
DATABOUNDARY option (spline), 404
DEGREE option (polynomial), 400
DEGREE option (spline), 404
DESIGNROLE option (lag), 397
DETAILS option (lag), 397
DETAILS option (multimember), 399
DETAILS option (polynomial), 400
DETAILS option (spline), 404
KNOTMAX option (spline), 404
KNOTMETHOD option (spline), 404
KNOTMIN option (spline), 406
LABELSTYLE option (polynomial), 400
lag effect, 395
MDEGREE option (polynomial), 401
multimember effect, 398
NATURALCUBIC option (spline), 406
NLAG option (lag), 398
NOEFFECT option (multimember), 399
NOSEPARATE option (polynomial), 401
PERIOD option (lag), 397
polynomial effect, 399
SEPARATE option (spline), 406
spline effect, 403
SPLIT option (spline), 406
STANDARDIZE option (polynomial), 401
WITHIN option (lag), 397
HPMIXED procedure, NLOPTIONS statement
ABSCONV option, 484
ABSFCONV option, 484
ABSGCONV option, 484
ABSGTOL option, 484
ABSTOL option, 484
ABSXCONV option, 484
ABSXTOL option, 484
ASINGULAR= option, 485
FCONV option, 485
FCONV2 option, 486
FSIZE option, 486
FTOL option, 485
FTOL2 option, 486
GCONV option, 486
GCONV2 option, 487
GTOL option, 486
GTOL2 option, 487
HESCAL option, 487
HS option, 487
INHESSIAN option, 488
INSTEP option, 488
LCDEACT= option, 488
LCEPSILON= option, 489
LCSINGULAR= option, 489
LINESEARCH option, 489
LIS option, 489
LSP option, 490
LSPRECISION option, 490
MAXFU option, 490
MAXFUNC option, 490
MAXIT option, 490
MAXITER option, 490
MAXSTEP option, 491
MAXTIME option, 491
MINIT option, 491
MINITER option, 491
MSINGULAR= option, 491
REST option, 491
RESTART option, 491
SINGULAR= option, 492
SOCKET option, 492
TECH option, 492
TECHNIQUE option, 492
UPD option, 493
XSIZE option, 494
XTOL option, 494
HS option
NLOPTIONS statement (CALIS), 487
NLOPTIONS statement (GLIMMIX), 487
NLOPTIONS statement (HPMIXED), 487
NLOPTIONS statement (PHREG), 487
NLOPTIONS statement (SURVEYPHREG), 487
NLOPTIONS statement (VARIOGRAM), 487
HTYPE= option
TEST statement (LIFEREG), 504
TEST statement (ORTHOREG), 504
TEST statement (PLM), 504
TEST statement (PROBIT), 504
TEST statement (SURVEYPHREG), 504
TEST statement (SURVEYREG), 504
ILINK option
EFFECTPLOT statement, 416
ESTIMATE statement (LIFEREG), 443
ESTIMATE statement (LOGISTIC), 443
ESTIMATE statement (PLM), 443
ESTIMATE statement (PROBIT), 443
ESTIMATE statement (SURVEYLOGISTIC),
443
LSMEANS statement (GENMOD), 461
LSMEANS statement (LIFEREG), 461
LSMEANS statement (LOGISTIC), 461
LSMEANS statement (PLM), 461
LSMEANS statement (PROBIT), 461
LSMEANS statement (SURVEYLOGISTIC),
461
LSMESTIMATE statement (GENMOD), 475
LSMESTIMATE statement (LIFEREG), 475
LSMESTIMATE statement (LOGISTIC), 475
LSMESTIMATE statement (PLM), 475
LSMESTIMATE statement (PROBIT), 475
LSMESTIMATE statement
(SURVEYLOGISTIC), 475
SLICE statement (GENMOD), 461
SLICE statement (GLIMMIX), 461
SLICE statement (LIFEREG), 461
SLICE statement (LOGISTIC), 461
SLICE statement (PLM), 461
SLICE statement (PROBIT), 461
SLICE statement (SURVEYLOGISTIC), 461
IMPUTE option
CODE statement (GENMOD), 392
CODE statement (GLIMMIX), 392
CODE statement (GLM), 392
CODE statement (GLMSELECT), 392
CODE statement (LOGISTIC), 392
CODE statement (MIXED), 392
CODE statement (PLM), 392
CODE statement (REG), 392
INDIVIDUAL option
EFFECTPLOT statement, 416
INHESS option
NLOPTIONS statement (CALIS), 488
NLOPTIONS statement (GLIMMIX), 488
NLOPTIONS statement (HPMIXED), 488
NLOPTIONS statement (PHREG), 488
NLOPTIONS statement (SURVEYPHREG), 488
NLOPTIONS statement (VARIOGRAM), 488
INHESSIAN option
NLOPTIONS statement (GLIMMIX), 488
NLOPTIONS statement (HPMIXED), 488
NLOPTIONS statement (PHREG), 488
NLOPTIONS statement (SURVEYPHREG), 488
NLOPTIONS statement (TCLAIS), 488
NLOPTIONS statement (VARIOGRAM), 488
INSTEP option
NLOPTIONS statement (CALIS), 488
NLOPTIONS statement (GLIMMIX), 488
NLOPTIONS statement (HPMIXED), 488
NLOPTIONS statement (PHREG), 488
NLOPTIONS statement (SURVEYPHREG), 488
NLOPTIONS statement (VARIOGRAM), 488
INTERCEPT option
TEST statement (LIFEREG), 504
TEST statement (ORTHOREG), 504
TEST statement (PLM), 504
TEST statement (PROBIT), 504
TEST statement (SURVEYPHREG), 504
TEST statement (SURVEYREG), 504
JOINT option
ESTIMATE statement (LIFEREG), 444
ESTIMATE statement (LOGISTIC), 444
ESTIMATE statement (ORTHOREG), 444
ESTIMATE statement (PHREG), 444
ESTIMATE statement (PLM), 444
ESTIMATE statement (PROBIT), 444
ESTIMATE statement (QUANTREG), 444
ESTIMATE statement (SURVEYLOGISTIC),
444
ESTIMATE statement (SURVEYPHREG), 444
ESTIMATE statement (SURVEYREG), 444
LSMESTIMATE statement (GENMOD), 476
LSMESTIMATE statement (LIFEREG), 476
LSMESTIMATE statement (LOGISTIC), 476
LSMESTIMATE statement (MIXED), 476
LSMESTIMATE statement (ORTHOREG), 476
LSMESTIMATE statement (PHREG), 476
LSMESTIMATE statement (PLM), 476
LSMESTIMATE statement (PROBIT), 476
LSMESTIMATE statement
(SURVEYLOGISTIC), 476
LSMESTIMATE statement (SURVEYPHREG),
476
LSMESTIMATE statement (SURVEYREG),
476
KNOTMAX option
EFFECT statement, spline (GLIMMIX), 404
EFFECT statement, spline (GLMSELECT), 404
EFFECT statement, spline (HPMIXED), 404
EFFECT statement, spline (LOGISTIC), 404
EFFECT statement, spline (ORTHOREG), 404
EFFECT statement, spline (PHREG), 404
EFFECT statement, spline (PLS), 404
EFFECT statement, spline (QUANTLIFE), 404
EFFECT statement, spline (QUANTREG), 404
EFFECT statement, spline (QUANTSELECT),
404
EFFECT statement, spline (ROBUSTREG), 404
EFFECT statement, spline
(SURVEYLOGISTIC), 404
EFFECT statement, spline (SURVEYREG), 404
KNOTMETHOD option
EFFECT statement, spline (GLIMMIX), 404
EFFECT statement, spline (GLMSELECT), 404
EFFECT statement, spline (HPMIXED), 404
EFFECT statement, spline (LOGISTIC), 404
EFFECT statement, spline (ORTHOREG), 404
EFFECT statement, spline (PHREG), 404
EFFECT statement, spline (PLS), 404
EFFECT statement, spline (QUANTLIFE), 404
EFFECT statement, spline (QUANTREG), 404
EFFECT statement, spline (QUANTSELECT),
404
EFFECT statement, spline (ROBUSTREG), 404
EFFECT statement, spline
(SURVEYLOGISTIC), 404
EFFECT statement, spline (SURVEYREG), 404
KNOTMIN option
EFFECT statement, spline (GLIMMIX), 406
EFFECT statement, spline (GLMSELECT), 406
EFFECT statement, spline (HPMIXED), 406
EFFECT statement, spline (LOGISTIC), 406
EFFECT statement, spline (ORTHOREG), 406
EFFECT statement, spline (PHREG), 406
EFFECT statement, spline (PLS), 406
EFFECT statement, spline (QUANTLIFE), 406
EFFECT statement, spline (QUANTREG), 406
EFFECT statement, spline (QUANTSELECT),
406
EFFECT statement, spline (ROBUSTREG), 406
EFFECT statement, spline
(SURVEYLOGISTIC), 406
EFFECT statement, spline (SURVEYREG), 406
LABELSTYLE option
EFFECT statement, polynomial (GLIMMIX),
400
EFFECT statement, polynomial
(GLMSELECT), 400
EFFECT statement, polynomial (HPMIXED),
400
EFFECT statement, polynomial (LOGISTIC),
400
EFFECT statement, polynomial (ORTHOREG),
400
EFFECT statement, polynomial (PHREG), 400
EFFECT statement, polynomial (PLS), 400
EFFECT statement, polynomial (QUANTLIFE),
400
EFFECT statement, polynomial (QUANTREG),
400
EFFECT statement, polynomial
(QUANTSELECT), 400
EFFECT statement, polynomial
(ROBUSTREG), 400
EFFECT statement, polynomial
(SURVEYLOGISTIC), 400
EFFECT statement, polynomial
(SURVEYREG), 400
LCDEACT= option
NLOPTIONS statement (CALIS), 488
NLOPTIONS statement (GLIMMIX), 488
NLOPTIONS statement (HPMIXED), 488
NLOPTIONS statement (PHREG), 488
NLOPTIONS statement (SURVEYPHREG), 488
NLOPTIONS statement (VARIOGRAM), 488
LCEPSILON= option
NLOPTIONS statement (CALIS), 489
NLOPTIONS statement (GLIMMIX), 489
NLOPTIONS statement (HPMIXED), 489
NLOPTIONS statement (PHREG), 489
NLOPTIONS statement (SURVEYPHREG), 489
NLOPTIONS statement (VARIOGRAM), 489
LCSINGULAR= option
NLOPTIONS statement (CALIS), 489
NLOPTIONS statement (GLIMMIX), 489
NLOPTIONS statement (HPMIXED), 489
NLOPTIONS statement (PHREG), 489
NLOPTIONS statement (SURVEYPHREG), 489
NLOPTIONS statement (VARIOGRAM), 489
LIFEREG procedure, ESTIMATE statement
ADJUST= option, 440
ALPHA= option, 441
CL option, 442
CORR option, 442
COV option, 442
DIVISOR= option, 442
E option, 443
EXP option, 443
ILINK option, 443
JOINT option, 444
LOWER option, 445
NOFILL option, 445
ODS graph names, 452
ODS table names, 452
PLOTS= option, 445
SEED= option, 446
SINGULAR= option, 446
STEPDOWN option, 446
TESTVALUE option, 448
UPPER option, 448
LIFEREG procedure, LSMEANS statement
ADJUST= option, 456
ALPHA= option, 458
AT= option, 458
BYLEVEL option, 459
CL option, 459
CORR option, 459
COV option, 459
DIFF option, 460
E option, 461
EXP option, 461
ILINK option, 461
LINES option, 461
MEANS or NOMEANS option, 462
OBSMARGINS= option, 462
ODDSRATIO option, 462
ODS graph names, 468
ODS table names, 468
PDIFF option, 463
PLOTS= option, 463
SEED= option, 466
SINGULAR= option, 467
STEPDOWN option, 467
LIFEREG procedure, LSMESIIMATE statement
ADJUST= option, 473
ALPHA= option, 473
AT= option, 473
BYLEVEL option, 473
CATEGORY= option, 473
CL option, 474
COV option, 474
DIVISOR= option, 474
E option, 475
ELSM option, 475
ILINK option, 475
JOINT option, 476
LOWER option, 477
OBSMARGINS= option, 477
ODS graph names, 481
ODS table names, 481
PLOTS= option, 477
SEED= option, 478
SINGULAR= option, 479
STEPDOWN option, 479
TESTVALUE= option, 480
UPPER option, 480
LIFEREG procedure, SLICE statement
ADJUST= option, 456
ALPHA= option, 458
AT= option, 458
BYLEVEL option, 459
CL option, 459
CORR option, 459
COV option, 459
DIFF option, 460
E option, 461
EXP option, 461
ILINK option, 461
LINES option, 461
MEANS or NOMEANS option, 462
NOF option, 501
OBSMARGINS= option, 462
ODS table names, 501
PDIFF option, 463
PLOTS= option, 463
SEED= option, 466
SIMPLE= option, 500
SINGULAR= option, 467
SLICEBY= option, 500
STEPDOWN option, 467
LIFEREG procedure, TEST statement
CHISQ option, 503
DDF= option, 503
E option, 503
E1 option, 503
E2 option, 504
E3 option, 504
HTYPE= option, 504
INTERCEPT option, 504
ODS table names, 504
LIMITS option
EFFECTPLOT statement, 416
LINES option
LSMEANS statement (GENMOD), 461
LSMEANS statement (LIFEREG), 461
LSMEANS statement (LOGISTIC), 461
LSMEANS statement (ORTHOREG), 461
LSMEANS statement (PHREG), 461
LSMEANS statement (PLM), 461
LSMEANS statement (PROBIT), 461
LSMEANS statement (SURVEYLOGISTIC),
461
LSMEANS statement (SURVEYPHREG), 461
LSMEANS statement (SURVEYREG), 461
SLICE statement (GENMOD), 461
SLICE statement (GLIMMIX), 461
SLICE statement (LIFEREG), 461
SLICE statement (LOGISTIC), 461
SLICE statement (MIXED), 461
SLICE statement (ORTHOREG), 461
SLICE statement (PHREG), 461
SLICE statement (PLM), 461
SLICE statement (PROBIT), 461
SLICE statement (SURVEYLOGISTIC), 461
SLICE statement (SURVEYPHREG), 461
SLICE statement (SURVEYREG), 461
LINESEARCH option
NLOPTIONS statement (CALIS), 489
NLOPTIONS statement (GLIMMIX), 489
NLOPTIONS statement (HPMIXED), 489
NLOPTIONS statement (PHREG), 489
NLOPTIONS statement (SURVEYPHREG), 489
NLOPTIONS statement (VARIOGRAM), 489
LINESIZE= option
CODE statement (GENMOD), 392
CODE statement (GLIMMIX), 392
CODE statement (GLM), 392
CODE statement (GLMSELECT), 392
CODE statement (LOGISTIC), 392
CODE statement (MIXED), 392
CODE statement (PLM), 392
CODE statement (REG), 392
LINK option
EFFECTPLOT statement, 416
LIS option
NLOPTIONS statement (CALIS), 489
NLOPTIONS statement (GLIMMIX), 489
NLOPTIONS statement (HPMIXED), 489
NLOPTIONS statement (PHREG), 489
NLOPTIONS statement (SURVEYPHREG), 489
NLOPTIONS statement (VARIOGRAM), 489
LOGISTIC procedure, CODE statement
CATALOG= option, 391
DUMMIES option, 391
ERRORS option, 392
FILE= option, 392
FORMAT= option, 392
GROUP= option, 392
IMPUTE option, 392
LINESIZE= option, 392
LOOKUP= option, 392
NODUMMIES option, 391
NOERRORS option, 392
NORESIDUAL option, 393
RESIDUAL option, 393
LOGISTIC procedure, EFFECT statement
BASIS option (spline), 403
collection effect, 395
DATABOUNDARY option (spline), 404
DEGREE option (polynomial), 400
DEGREE option (spline), 404
DESIGNROLE option (lag), 397
DETAILS option (lag), 397
DETAILS option (multimember), 399
DETAILS option (polynomial), 400
DETAILS option (spline), 404
KNOTMAX option (spline), 404
KNOTMETHOD option (spline), 404
KNOTMIN option (spline), 406
LABELSTYLE option (polynomial), 400
lag effect, 395
MDEGREE option (polynomial), 401
multimember effect, 398
NATURALCUBIC option (spline), 406
NLAG option (lag), 398
NOEFFECT option (multimember), 399
NOSEPARATE option (polynomial), 401
PERIOD option (lag), 397
polynomial effect, 399
SEPARATE option (spline), 406
spline effect, 403
SPLIT option (spline), 406
STANDARDIZE option (polynomial), 401
WITHIN option (lag), 397
LOGISTIC procedure, EFFECTPLOT statement
ALPHA= option, 414
AT option, 414
ATLEN= option, 415
ATORDER= option, 415
CLI option, 415
CLM option, 415
CLUSTER option, 415
CONNECT option, 416
EXTEND= option, 416
GRIDSIZE= option, 416
ILINK option, 416
INDIVIDUAL option, 416
LIMITS option, 416
LINK option, 416
MOFF option, 416
NCOLS= option, 416
NOCLI option, 417
NOCLM option, 417
NOCLUSTER option, 417
NOCONNECT option, 417
NOLIMITS option, 417
NOOBS option, 417
NROWS= option, 417
OBS option, 417
PLOTBY= option, 420
PLOTBYLEN= option, 421
POLYBAR option, 421
PREDLABEL= option, 421
SHOWCLEGEND option, 421
SLICEBY= option, 421
SMOOTH option, 421
UNPACK option, 421
X= option, 421
Y= option, 422
YRANGE= option, 422
LOGISTIC procedure, ESTIMATE statement
ADJUST= option, 440
ALPHA= option, 441
CATEGORY= option, 441
CL option, 442
CORR option, 442
COV option, 442
DIVISOR= option, 442
E option, 443
EXP option, 443
ILINK option, 443
JOINT option, 444
LOWER option, 445
NOFILL option, 445
ODS table names, 452
SEED= option, 446
SINGULAR= option, 446
STEPDOWN option, 446
TESTVALUE option, 448
UPPER option, 448
LOGISTIC procedure, LSMEANS statement
ADJUST= option, 456
ALPHA= option, 458
AT= option, 458
BYLEVEL option, 459
CL option, 459
CORR option, 459
COV option, 459
DIFF option, 460
E option, 461
EXP option, 461
ILINK option, 461
LINES option, 461
MEANS or NOMEANS option, 462
OBSMARGINS= option, 462
ODDSRATIO option, 462
ODS graph names, 468
ODS table names, 468
PDIFF option, 463
PLOTS= option, 463
SEED= option, 466
SINGULAR= option, 467
STEPDOWN option, 467
LOGISTIC procedure, LSMESIIMATE statement
ADJUST= option, 473
ALPHA= option, 473
AT= option, 473
BYLEVEL option, 473
CATEGORY= option, 473
CL option, 474
CORR option, 474
COV option, 474
DIVISOR= option, 474
E option, 475
ELSM option, 475
EXP option, 475
ILINK option, 475
JOINT option, 476
LOWER option, 477
OBSMARGINS= option, 477
ODS table names, 481
PLOTS= option, 477
SEED= option, 478
SINGULAR= option, 479
STEPDOWN option, 479
TESTVALUE= option, 480
UPPER option, 480
LOGISTIC procedure, SLICE statement
ADJUST= option, 456
ALPHA= option, 458
AT= option, 458
BYLEVEL option, 459
CL option, 459
CORR option, 459
COV option, 459
DIFF option, 460
E option, 461
EXP option, 461
ILINK option, 461
LINES option, 461
MEANS or NOMEANS option, 462
NOF option, 501
OBSMARGINS= option, 462
ODDSRATIO option, 462
ODS table names, 501
PDIFF option, 463
PLOTS= option, 463
SEED= option, 466
SIMPLE= option, 500
SINGULAR= option, 467
SLICEBY= option, 500
STEPDOWN option, 467
LOOKUP= option
CODE statement (GENMOD), 392
CODE statement (GLIMMIX), 392
CODE statement (GLM), 392
CODE statement (GLMSELECT), 392
CODE statement (LOGISTIC), 392
CODE statement (MIXED), 392
CODE statement (PLM), 392
CODE statement (REG), 392
LOWER option
ESTIMATE statement (LIFEREG), 445
ESTIMATE statement (LOGISTIC), 445
ESTIMATE statement (ORTHOREG), 445
ESTIMATE statement (PHREG), 445
ESTIMATE statement (PLM), 445
ESTIMATE statement (PROBIT), 445
ESTIMATE statement (QUANTREG), 445
ESTIMATE statement (SURVEYLOGISTIC),
445
ESTIMATE statement (SURVEYPHREG), 445
ESTIMATE statement (SURVEYREG), 445
LSMESTIMATE statement (GENMOD), 477
LSMESTIMATE statement (LIFEREG), 477
LSMESTIMATE statement (LOGISTIC), 477
LSMESTIMATE statement (MIXED), 477
LSMESTIMATE statement (ORTHOREG), 477
LSMESTIMATE statement (PHREG), 477
LSMESTIMATE statement (PLM), 477
LSMESTIMATE statement (PROBIT), 477
LSMESTIMATE statement
(SURVEYLOGISTIC), 477
LSMESTIMATE statement (SURVEYPHREG),
477
LSMESTIMATE statement (SURVEYREG),
477
LSMEANS statement
GENMOD procedure, 453
LIFEREG procedure, 453
LOGISTIC procedure, 453
ORTHOREG procedure, 453
PHREG procedure, 453
PLM procedure, 453
PROBIT procedure, 453
SURVEYLOGISTIC procedure, 453
SURVEYPHREG procedure, 453
SURVEYREG procedure, 453
LSMESTIMATE statement
GENMOD procedure, 470
LIFEREG procedure, 470
LOGISTIC procedure, 470
MIXED procedure, 470
ORTHOREG procedure, 470
PHREG procedure, 470
PLM procedure, 470
PROBIT procedure, 470
SURVEYLOGISTIC procedure, 470
SURVEYPHREG procedure, 470
SURVEYREG procedure, 470
LSP option
NLOPTIONS statement (CALIS), 490
NLOPTIONS statement (GLIMMIX), 490
NLOPTIONS statement (HPMIXED), 490
NLOPTIONS statement (PHREG), 490
NLOPTIONS statement (SURVEYPHREG), 490
NLOPTIONS statement (VARIOGRAM), 490
LSPRECISION option
NLOPTIONS statement (CALIS), 490
NLOPTIONS statement (GLIMMIX), 490
NLOPTIONS statement (HPMIXED), 490
NLOPTIONS statement (PHREG), 490
NLOPTIONS statement (SURVEYPHREG), 490
NLOPTIONS statement (VARIOGRAM), 490
MAXFU option
NLOPTIONS statement (CALIS), 490
NLOPTIONS statement (GLIMMIX), 490
NLOPTIONS statement (HPMIXED), 490
NLOPTIONS statement (PHREG), 490
NLOPTIONS statement (SURVEYPHREG), 490
NLOPTIONS statement (VARIOGRAM), 490
MAXFUNC option
NLOPTIONS statement (CALIS), 490
NLOPTIONS statement (GLIMMIX), 490
NLOPTIONS statement (HPMIXED), 490
NLOPTIONS statement (PHREG), 490
NLOPTIONS statement (SURVEYPHREG), 490
NLOPTIONS statement (VARIOGRAM), 490
MAXIT option
NLOPTIONS statement (CALIS), 490
NLOPTIONS statement (GLIMMIX), 490
NLOPTIONS statement (HPMIXED), 490
NLOPTIONS statement (PHREG), 490
NLOPTIONS statement (SURVEYPHREG), 490
NLOPTIONS statement (VARIOGRAM), 490
MAXITER option
NLOPTIONS statement (CALIS), 490
NLOPTIONS statement (GLIMMIX), 490
NLOPTIONS statement (HPMIXED), 490
NLOPTIONS statement (PHREG), 490
NLOPTIONS statement (SURVEYPHREG), 490
NLOPTIONS statement (VARIOGRAM), 490
MAXSTEP option
NLOPTIONS statement (CALIS), 491
NLOPTIONS statement (GLIMMIX), 491
NLOPTIONS statement (HPMIXED), 491
NLOPTIONS statement (PHREG), 491
NLOPTIONS statement (SURVEYPHREG), 491
NLOPTIONS statement (VARIOGRAM), 491
MAXTIME option
NLOPTIONS statement (CALIS), 491
NLOPTIONS statement (GLIMMIX), 491
NLOPTIONS statement (HPMIXED), 491
NLOPTIONS statement (PHREG), 491
NLOPTIONS statement (SURVEYPHREG), 491
NLOPTIONS statement (VARIOGRAM), 491
MDEGREE option
EFFECT statement, polynomial (GLIMMIX),
401
EFFECT statement, polynomial
(GLMSELECT), 401
EFFECT statement, polynomial (HPMIXED),
401
EFFECT statement, polynomial (LOGISTIC),
401
EFFECT statement, polynomial (ORTHOREG),
401
EFFECT statement, polynomial (PHREG), 401
EFFECT statement, polynomial (PLS), 401
EFFECT statement, polynomial (QUANTLIFE),
401
EFFECT statement, polynomial (QUANTREG),
401
EFFECT statement, polynomial
(QUANTSELECT), 401
EFFECT statement, polynomial
(ROBUSTREG), 401
EFFECT statement, polynomial
(SURVEYLOGISTIC), 401
EFFECT statement, polynomial
(SURVEYREG), 401
MEANS or NOMEANS option
LSMEANS statement (GENMOD), 462
LSMEANS statement (LIFEREG), 462
LSMEANS statement (LOGISTIC), 462
LSMEANS statement (ORTHOREG), 462
LSMEANS statement (PHREG), 462
LSMEANS statement (PLM), 462
LSMEANS statement (PROBIT), 462
LSMEANS statement (SURVEYLOGISTIC),
462
LSMEANS statement (SURVEYPHREG), 462
LSMEANS statement (SURVEYREG), 462
SLICE statement (GENMOD), 462
SLICE statement (GLIMMIX), 462
SLICE statement (LIFEREG), 462
SLICE statement (LOGISTIC), 462
SLICE statement (MIXED), 462
SLICE statement (ORTHOREG), 462
SLICE statement (PHREG), 462
SLICE statement (PLM), 462
SLICE statement (PROBIT), 462
SLICE statement (SURVEYLOGISTIC), 462
SLICE statement (SURVEYPHREG), 462
SLICE statement (SURVEYREG), 462
MINIT option
NLOPTIONS statement (CALIS), 491
NLOPTIONS statement (GLIMMIX), 491
NLOPTIONS statement (HPMIXED), 491
NLOPTIONS statement (PHREG), 491
NLOPTIONS statement (SURVEYPHREG), 491
NLOPTIONS statement (VARIOGRAM), 491
MINITER option
NLOPTIONS statement (CALIS), 491
NLOPTIONS statement (GLIMMIX), 491
NLOPTIONS statement (HPMIXED), 491
NLOPTIONS statement (PHREG), 491
NLOPTIONS statement (SURVEYPHREG), 491
NLOPTIONS statement (VARIOGRAM), 491
MIXED procedure, CODE statement
CATALOG= option, 391
DUMMIES option, 391
ERRORS option, 392
FILE= option, 392
FORMAT= option, 392
GROUP= option, 392
IMPUTE option, 392
LINESIZE= option, 392
LOOKUP= option, 392
NODUMMIES option, 391
NOERRORS option, 392
NORESIDUAL option, 393
RESIDUAL option, 393
MIXED procedure, LSMESIIMATE statement
ADJDFE= option, 472
ADJUST= option, 473
ALPHA= option, 473
AT= option, 473
BYLEVEL option, 473
CHISQ option, 474
CL option, 474
CORR option, 474
COV option, 474
DF= option, 474
DIVISOR= option, 474
E option, 475
ELSM option, 475
JOINT option, 476
LOWER option, 477
OBSMARGINS= option, 477
ODS table names, 481
PLOTS= option, 477
SEED= option, 478
SINGULAR= option, 479
STEPDOWN option, 479
TESTVALUE= option, 480
UPPER option, 480
MIXED procedure, SLICE statement
ADJDFE= option, 455
ADJUST= option, 456
ALPHA= option, 458
AT= option, 458
BYLEVEL option, 459
CL option, 459
CORR option, 459
COV option, 459
DF= option, 460
DIFF option, 460
E option, 461
LINES option, 461
MEANS or NOMEANS option, 462
NOF option, 501
OBSMARGINS= option, 462
ODS graph names, 468
ODS table names, 501
PDIFF option, 463
PLOTS= option, 463
SEED= option, 466
SIMPLE= option, 500
SINGULAR= option, 467
SLICEBY= option, 500
STEPDOWN option, 467
MOFF option
EFFECTPLOT statement, 416
MSINGULAR= option
NLOPTIONS statement (CALIS), 491
NLOPTIONS statement (GLIMMIX), 491
NLOPTIONS statement (HPMIXED), 491
NLOPTIONS statement (PHREG), 491
NLOPTIONS statement (SURVEYPHREG), 491
NLOPTIONS statement (VARIOGRAM), 491
NATURALCUBIC option
EFFECT statement, spline (GLIMMIX), 406
EFFECT statement, spline (GLMSELECT), 406
EFFECT statement, spline (HPMIXED), 406
EFFECT statement, spline (LOGISTIC), 406
EFFECT statement, spline (ORTHOREG), 406
EFFECT statement, spline (PHREG), 406
EFFECT statement, spline (PLS), 406
EFFECT statement, spline (QUANTLIFE), 406
EFFECT statement, spline (QUANTREG), 406
EFFECT statement, spline (QUANTSELECT),
406
EFFECT statement, spline (ROBUSTREG), 406
EFFECT statement, spline
(SURVEYLOGISTIC), 406
EFFECT statement, spline (SURVEYREG), 406
NCOLS= option
EFFECTPLOT statement, 416
NLAG option
EFFECT statement, lag (GLIMMIX), 398
EFFECT statement, lag (GLMSELECT), 398
EFFECT statement, lag (HPMIXED), 398
EFFECT statement, lag (LOGISTIC), 398
EFFECT statement, lag (ORTHOREG), 398
EFFECT statement, lag (PHREG), 398
EFFECT statement, lag (PLS), 398
EFFECT statement, lag (QUANTLIFE), 398
EFFECT statement, lag (QUANTREG), 398
EFFECT statement, lag (QUANTSELECT), 398
EFFECT statement, lag (ROBUSTREG), 398
EFFECT statement, lag (SURVEYLOGISTIC),
398
EFFECT statement, lag (SURVEYREG), 398
NLMIXED procedure, NLOPTIONS statement
VSINGULAR= option, 494
NLOPTIONS statement
CALIS procedure, 482
GLIMMIX procedure, 482
HPMIXED procedure, 482
PHREG procedure, 482
SURVEYPHREG procedure, 482
VARIOGRAM procedure, 482
NOCLI option
EFFECTPLOT statement, 417
NOCLM option
EFFECTPLOT statement, 417
NOCLUSTER option
EFFECTPLOT statement, 417
NOCONNECT option
EFFECTPLOT statement, 417
NODUMMIES option
CODE statement (GENMOD), 391
CODE statement (GLIMMIX), 391
CODE statement (GLM), 391
CODE statement (GLMSELECT), 391
CODE statement (LOGISTIC), 391
CODE statement (MIXED), 391
CODE statement (PLM), 391
CODE statement (REG), 391
NOEFFECT option
EFFECT statement, multimember (GLIMMIX),
399
EFFECT statement, multimember
(GLMSELECT), 399
EFFECT statement, multimember (HPMIXED),
399
EFFECT statement, multimember (LOGISTIC),
399
EFFECT statement, multimember
(ORTHOREG), 399
EFFECT statement, multimember (PHREG), 399
EFFECT statement, multimember (PLS), 399
EFFECT statement, multimember
(QUANTLIFE), 399
EFFECT statement, multimember
(QUANTREG), 399
EFFECT statement, multimember
(QUANTSELECT), 399
EFFECT statement, multimember
(ROBUSTREG), 399
EFFECT statement, multimember
(SURVEYLOGISTIC), 399
EFFECT statement, multimember
(SURVEYREG), 399
NOERRORS option
CODE statement (GENMOD), 392
CODE statement (GLIMMIX), 392
CODE statement (GLM), 392
CODE statement (GLMSELECT), 392
CODE statement (LOGISTIC), 392
CODE statement (MIXED), 392
CODE statement (PLM), 392
CODE statement (REG), 392
NOF option
SLICE statement (GENMOD), 501
SLICE statement (GLIMMIX), 501
SLICE statement (LIFEREG), 501
SLICE statement (LOGISTIC), 501
SLICE statement (MIXED), 501
SLICE statement (ORTHOREG), 501
SLICE statement (PHREG), 501
SLICE statement (PLM), 501
SLICE statement (PROBIT), 501
SLICE statement (SURVEYLOGISTIC), 501
SLICE statement (SURVEYPHREG), 501
SLICE statement (SURVEYREG), 501
NOFILL option
ESTIMATE statement (LIFEREG), 445
ESTIMATE statement (LOGISTIC), 445
ESTIMATE statement (ORTHOREG), 445
ESTIMATE statement (PHREG), 445
ESTIMATE statement (PLM), 445
ESTIMATE statement (PROBIT), 445
ESTIMATE statement (QUANTREG), 445
ESTIMATE statement (SURVEYLOGISTIC),
445
ESTIMATE statement (SURVEYPHREG), 445
ESTIMATE statement (SURVEYREG), 445
NOLIMITS option
EFFECTPLOT statement, 417
NOOBS option
EFFECTPLOT statement, 417
NORESIDUAL option
CODE statement (GENMOD), 393
CODE statement (GLIMMIX), 393
CODE statement (GLM), 393
CODE statement (GLMSELECT), 393
CODE statement (LOGISTIC), 393
CODE statement (MIXED), 393
CODE statement (PLM), 393
CODE statement (REG), 393
NOSEPARATE option
EFFECT statement, polynomial (GLIMMIX),
401
EFFECT statement, polynomial
(GLMSELECT), 401
EFFECT statement, polynomial (HPMIXED),
401
EFFECT statement, polynomial (LOGISTIC),
401
EFFECT statement, polynomial (ORTHOREG),
401
EFFECT statement, polynomial (PHREG), 401
EFFECT statement, polynomial (PLS), 401
EFFECT statement, polynomial (QUANTLIFE),
401
EFFECT statement, polynomial (QUANTREG),
401
EFFECT statement, polynomial
(QUANTSELECT), 401
EFFECT statement, polynomial
(ROBUSTREG), 401
EFFECT statement, polynomial
(SURVEYLOGISTIC), 401
EFFECT statement, polynomial
(SURVEYREG), 401
NROWS= option
EFFECTPLOT statement, 417
OBS option
EFFECTPLOT statement, 417
OBSMARGINS= option
LSMEANS statement (GENMOD), 462
LSMEANS statement (LIFEREG), 462
LSMEANS statement (LOGISTIC), 462
LSMEANS statement (ORTHOREG), 462
LSMEANS statement (PHREG), 462
LSMEANS statement (PLM), 462
LSMEANS statement (PROBIT), 462
LSMEANS statement (SURVEYLOGISTIC),
462
LSMEANS statement (SURVEYPHREG), 462
LSMEANS statement (SURVEYREG), 462
LSMESTIMATE statement (GENMOD), 477
LSMESTIMATE statement (LIFEREG), 477
LSMESTIMATE statement (LOGISTIC), 477
LSMESTIMATE statement (MIXED), 477
LSMESTIMATE statement (ORTHOREG), 477
LSMESTIMATE statement (PHREG), 477
LSMESTIMATE statement (PLM), 477
LSMESTIMATE statement (PROBIT), 477
LSMESTIMATE statement
(SURVEYLOGISTIC), 477
LSMESTIMATE statement (SURVEYPHREG),
477
LSMESTIMATE statement (SURVEYREG),
477
SLICE statement (GENMOD), 462
SLICE statement (GLIMMIX), 462
SLICE statement (LIFEREG), 462
SLICE statement (LOGISTIC), 462
SLICE statement (MIXED), 462
SLICE statement (ORTHOREG), 462
SLICE statement (PHREG), 462
SLICE statement (PLM), 462
SLICE statement (PROBIT), 462
SLICE statement (SURVEYLOGISTIC), 462
SLICE statement (SURVEYPHREG), 462
SLICE statement (SURVEYREG), 462
ODDSRATIO option
LSMEANS statement (GENMOD), 462
LSMEANS statement (LIFEREG), 462
LSMEANS statement (LOGISTIC), 462
LSMEANS statement (PLM), 462
LSMEANS statement (PROBIT), 462
LSMEANS statement (SURVEYLOGISTIC),
462
SLICE statement (GENMOD), 462
SLICE statement (GLIMMIX), 462
SLICE statement (LIFEREG), 462
SLICE statement (LOGISTIC), 462
SLICE statement (PLM), 462
SLICE statement (PROBIT), 462
SLICE statement (SURVEYLOGISTIC), 462
ODS graph names
ESTIMATE statement (LIFEREG), 452
ESTIMATE statement (PHREG), 452
ESTIMATE statement (PLM), 452
LSMEANS statement (GENMOD), 468
LSMEANS statement (LIFEREG), 468
LSMEANS statement (LOGISTIC), 468
LSMEANS statement (ORTHOREG), 468
LSMEANS statement (PHREG), 468
LSMEANS statement (PLM), 468
LSMEANS statement (PROBIT), 468
LSMEANS statement (SURVEYLOGISTIC),
468
LSMEANS statement (SURVEYPHREG), 468
LSMEANS statement (SURVEYREG), 468
LSMESTIMATE statement (GENMOD), 481
LSMESTIMATE statement (LIFEREG), 481
LSMESTIMATE statement (PHREG), 481
LSMESTIMATE statement (PLM), 481
SLICE statement (GENMOD), 468
SLICE statement (GLIMMIX), 468
SLICE statement (LIFEREG), 468
SLICE statement (LOGISTIC), 468
SLICE statement (MIXED), 468
SLICE statement (ORTHOREG), 468
SLICE statement (PHREG), 468
SLICE statement (PLM), 468
SLICE statement (PROBIT), 468
SLICE statement (SURVEYLOGISTIC), 468
SLICE statement (SURVEYPHREG), 468
SLICE statement (SURVEYREG), 468
ODS table names
ESTIMATE statement (LIFEREG), 452
ESTIMATE statement (LOGISTIC), 452
ESTIMATE statement (ORTHOREG), 452
ESTIMATE statement (PHREG), 452
ESTIMATE statement (PLM), 452
ESTIMATE statement (PROBIT), 452
ESTIMATE statement (QUANTREG), 452
ESTIMATE statement (SURVEYLOGISTIC),
452
ESTIMATE statement (SURVEYPHREG), 452
ESTIMATE statement (SURVEYREG), 452
LSMEANS statement (GENMOD), 468
LSMEANS statement (LIFEREG), 468
LSMEANS statement (LOGISTIC), 468
LSMEANS statement (ORTHOREG), 468
LSMEANS statement (PHREG), 468
LSMEANS statement (PLM), 468
LSMEANS statement (PROBIT), 468
LSMEANS statement (SURVEYLOGISTIC),
468
LSMEANS statement (SURVEYPHREG), 468
LSMEANS statement (SURVEYREG), 468
LSMESTIMATE statement (GENMOD), 481
LSMESTIMATE statement (LIFEREG), 481
LSMESTIMATE statement (LOGISTIC), 481
LSMESTIMATE statement (MIXED), 481
LSMESTIMATE statement (ORTHOREG), 481
LSMESTIMATE statement (PHREG), 481
LSMESTIMATE statement (PLM), 481
LSMESTIMATE statement (PROBIT), 481
LSMESTIMATE statement
(SURVEYLOGISTIC), 481
LSMESTIMATE statement (SURVEYPHREG),
481
LSMESTIMATE statement (SURVEYREG),
481
SLICE statement (GENMOD), 501
SLICE statement (GLIMMIX), 501
SLICE statement (LIFEREG), 501
SLICE statement (LOGISTIC), 501
SLICE statement (MIXED), 501
SLICE statement (ORTHOREG), 501
SLICE statement (PHREG), 501
SLICE statement (PLM), 501
SLICE statement (PROBIT), 501
SLICE statement (SURVEYLOGISTIC), 501
SLICE statement (SURVEYPHREG), 501
SLICE statement (SURVEYREG), 501
TEST statement (LIFEREG), 504
TEST statement (ORTHOREG), 504
TEST statement (PLM), 504
TEST statement (PROBIT), 504
TEST statement (SURVEYPHREG), 504
TEST statement (SURVEYREG), 504
ORTHOREG procedure, EFFECT statement
BASIS option (spline), 403
collection effect, 395
DATABOUNDARY option (spline), 404
DEGREE option (polynomial), 400
DEGREE option (spline), 404
DESIGNROLE option (lag), 397
DETAILS option (lag), 397
DETAILS option (multimember), 399
DETAILS option (polynomial), 400
DETAILS option (spline), 404
KNOTMAX option (spline), 404
KNOTMETHOD option (spline), 404
KNOTMIN option (spline), 406
LABELSTYLE option (polynomial), 400
lag effect, 395
MDEGREE option (polynomial), 401
multimember effect, 398
NATURALCUBIC option (spline), 406
NLAG option (lag), 398
NOEFFECT option (multimember), 399
NOSEPARATE option (polynomial), 401
PERIOD option (lag), 397
polynomial effect, 399
SEPARATE option (spline), 406
spline effect, 403
SPLIT option (spline), 406
STANDARDIZE option (polynomial), 401
WITHIN option (lag), 397
ORTHOREG procedure, EFFECTPLOT statement
ALPHA= option, 414
AT option, 414
ATLEN= option, 415
ATORDER= option, 415
CLI option, 415
CLM option, 415
CLUSTER option, 415
CONNECT option, 416
EXTEND= option, 416
GRIDSIZE= option, 416
ILINK option, 416
INDIVIDUAL option, 416
LIMITS option, 416
LINK option, 416
MOFF option, 416
NCOLS= option, 416
NOCLI option, 417
NOCLM option, 417
NOCLUSTER option, 417
NOCONNECT option, 417
NOLIMITS option, 417
NOOBS option, 417
NROWS= option, 417
OBS option, 417
PLOTBY= option, 420
PLOTBYLEN= option, 421
POLYBAR option, 421
PREDLABEL= option, 421
SHOWCLEGEND option, 421
SLICEBY= option, 421
SMOOTH option, 421
UNPACK option, 421
X= option, 421
Y= option, 422
YRANGE= option, 422
ORTHOREG procedure, ESTIMATE statement
ADJDFE= option, 440
ADJUST= option, 440
ALPHA= option, 441
CHISQ option, 442
CL option, 442
CORR option, 442
COV option, 442
DF= option, 442
DIVISOR= option, 442
E option, 443
JOINT option, 444
LOWER option, 445
NOFILL option, 445
ODS table names, 452
SEED= option, 446
SINGULAR= option, 446
STEPDOWN option, 446
TESTVALUE option, 448
UPPER option, 448
ORTHOREG procedure, LSMEANS statement
ADJDFE= option, 455
ADJUST= option, 456
ALPHA= option, 458
AT= option, 458
BYLEVEL option, 459
CL option, 459
CORR option, 459
COV option, 459
DF= option, 460
DIFF option, 460
E option, 461
LINES option, 461
MEANS or NOMEANS option, 462
OBSMARGINS= option, 462
ODS graph names, 468
ODS table names, 468
PDIFF option, 463
PLOTS= option, 463
SEED= option, 466
SINGULAR= option, 467
STEPDOWN option, 467
ORTHOREG procedure, LSMESIIMATE statement
ADJDFE= option, 472
ADJUST= option, 473
ALPHA= option, 473
AT= option, 473
BYLEVEL option, 473
CHISQ option, 474
CL option, 474
CORR option, 474
COV option, 474
DF= option, 474
DIVISOR= option, 474
E option, 475
ELSM option, 475
JOINT option, 476
LOWER option, 477
OBSMARGINS= option, 477
ODS table names, 481
PLOTS= option, 477
SEED= option, 478
SINGULAR= option, 479
STEPDOWN option, 479
TESTVALUE= option, 480
UPPER option, 480
ORTHOREG procedure, SLICE statement
ADJDFE= option, 455
ADJUST= option, 456
ALPHA= option, 458
AT= option, 458
BYLEVEL option, 459
CL option, 459
CORR option, 459
COV option, 459
DF= option, 460
DIFF option, 460
E option, 461
LINES option, 461
MEANS or NOMEANS option, 462
NOF option, 501
OBSMARGINS= option, 462
ODS table names, 501
PDIFF option, 463
PLOTS= option, 463
SEED= option, 466
SIMPLE= option, 500
SINGULAR= option, 467
SLICEBY= option, 500
STEPDOWN option, 467
ORTHOREG procedure, TEST statement
CHISQ option, 503
DDF= option, 503
E option, 503
E1 option, 503
E2 option, 504
E3 option, 504
HTYPE= option, 504
INTERCEPT option, 504
ODS table names, 504
PDIFF option
LSMEANS statement (GENMOD), 463
LSMEANS statement (LOGISTIC), 463
LSMEANS statement (ORTHOREG), 463
LSMEANS statement (PHREG), 463
LSMEANS statement (PLM), 463
LSMEANS statement (SURVEYLOGISTIC),
463
LSMEANS statement (SURVEYPHREG), 463
LSMEANS statement (SURVEYREG), 463
SLICE statement (GENMOD), 463
SLICE statement (GLIMMIX), 463
SLICE statement (LOGISTIC), 463
SLICE statement (MIXED), 463
SLICE statement (ORTHOREG), 463
SLICE statement (PHREG), 463
SLICE statement (PLM), 463
SLICE statement (SURVEYLOGISTIC), 463
SLICE statement (SURVEYPHREG), 463
SLICE statement (SURVEYREG), 463
PERIOD option
EFFECT statement, lag (GLIMMIX), 397
EFFECT statement, lag (GLMSELECT), 397
EFFECT statement, lag (HPMIXED), 397
EFFECT statement, lag (LOGISTIC), 397
EFFECT statement, lag (ORTHOREG), 397
EFFECT statement, lag (PHREG), 397
EFFECT statement, lag (PLS), 397
EFFECT statement, lag (QUANTLIFE), 397
EFFECT statement, lag (QUANTREG), 397
EFFECT statement, lag (QUANTSELECT), 397
EFFECT statement, lag (ROBUSTREG), 397
EFFECT statement, lag (SURVEYLOGISTIC),
397
EFFECT statement, lag (SURVEYREG), 397
PHREG procedure, EFFECT statement
BASIS option (spline), 403
collection effect, 395
DATABOUNDARY option (spline), 404
DEGREE option (polynomial), 400
DEGREE option (spline), 404
DESIGNROLE option (lag), 397
DETAILS option (lag), 397
DETAILS option (multimember), 399
DETAILS option (polynomial), 400
DETAILS option (spline), 404
KNOTMAX option (spline), 404
KNOTMETHOD option (spline), 404
KNOTMIN option (spline), 406
LABELSTYLE option (polynomial), 400
lag effect, 395
MDEGREE option (polynomial), 401
multimember effect, 398
NATURALCUBIC option (spline), 406
NLAG option (lag), 398
NOEFFECT option (multimember), 399
NOSEPARATE option (polynomial), 401
PERIOD option (lag), 397
polynomial effect, 399
SEPARATE option (spline), 406
spline effect, 403
SPLIT option (spline), 406
STANDARDIZE option (polynomial), 401
WITHIN option (lag), 397
PHREG procedure, ESTIMATE statement
ADJUST= option, 440
ALPHA= option, 441
CL option, 442
CORR option, 442
COV option, 442
DIVISOR= option, 442
E option, 443
EXP option, 443
JOINT option, 444
LOWER option, 445
NOFILL option, 445
ODS graph names, 452
ODS table names, 452
PLOTS= option, 445
SEED= option, 446
SINGULAR= option, 446
STEPDOWN option, 446
TESTVALUE option, 448
UPPER option, 448
PHREG procedure, LSMEANS statement
ADJUST= option, 456
ALPHA= option, 458
AT= option, 458
BYLEVEL option, 459
CL option, 459
CORR option, 459
COV option, 459
DIFF option, 460
E option, 461
EXP option, 461
LINES option, 461
MEANS or NOMEANS option, 462
OBSMARGINS= option, 462
ODS graph names, 468
ODS table names, 468
PDIFF option, 463
PLOTS= option, 463
SEED= option, 466
SINGULAR= option, 467
STEPDOWN option, 467
PHREG procedure, LSMESIIMATE statement
ADJUST= option, 473
ALPHA= option, 473
AT= option, 473
BYLEVEL option, 473
CL option, 474
CORR option, 474
COV option, 474
DIVISOR= option, 474
E option, 475
ELSM option, 475
EXP option, 475
JOINT option, 476
LOWER option, 477
OBSMARGINS= option, 477
ODS graph names, 481
ODS table names, 481
PLOTS= option, 477
SEED= option, 478
SINGULAR= option, 479
STEPDOWN option, 479
TESTVALUE= option, 480
UPPER option, 480
PHREG procedure, NLOPTIONS statement
ABSCONV option, 484
ABSFCONV option, 484
ABSGCONV option, 484
ABSGTOL option, 484
ABSTOL option, 484
ABSXCONV option, 484
ABSXTOL option, 484
ASINGULAR= option, 485
FCONV option, 485
FCONV2 option, 486
FSIZE option, 486
FTOL option, 485
FTOL2 option, 486
GCONV option, 486
GCONV2 option, 487
GTOL option, 486
GTOL2 option, 487
HESCAL option, 487
HS option, 487
INHESSIAN option, 488
INSTEP option, 488
LCDEACT= option, 488
LCEPSILON= option, 489
LCSINGULAR= option, 489
LINESEARCH option, 489
LSP option, 490
LSPRECISION option, 490
MAXFU option, 490
MAXFUNC option, 490
MAXIT option, 490
MAXITER option, 490
MAXSTEP option, 491
MAXTIME option, 491
MINIT option, 491
MINITER option, 491
MSINGULAR= option, 491
REST option, 491
RESTART option, 491
SINGULAR= option, 492
SOCKET option, 492
TECH option, 492
TECHNIQUE option, 492
UPD option, 493
VSINGULAR= option, 494
XSIZE option, 494
XTOL option, 494
PHREG procedure, SLICE statement
ADJUST= option, 456
ALPHA= option, 458
AT= option, 458
BYLEVEL option, 459
CL option, 459
CORR option, 459
COV option, 459
DIFF option, 460
E option, 461
EXP option, 461
LINES option, 461
MEANS or NOMEANS option, 462
NOF option, 501
OBSMARGINS= option, 462
ODS table names, 501
PDIFF option, 463
PLOTS= option, 463
SEED= option, 466
SIMPLE= option, 500
SINGULAR= option, 467
SLICEBY= option, 500
STEPDOWN option, 467
PLM procedure, CODE statement
CATALOG= option, 391
DUMMIES option, 391
ERRORS option, 392
FILE= option, 392
FORMAT= option, 392
GROUP= option, 392
IMPUTE option, 392
LINESIZE= option, 392
LOOKUP= option, 392
NODUMMIES option, 391
NOERRORS option, 392
NORESIDUAL option, 393
RESIDUAL option, 393
PLM procedure, EFFECTPLOT statement
ALPHA= option, 414
AT option, 414
ATLEN= option, 415
ATORDER= option, 415
CLI option, 415
CLM option, 415
CLUSTER option, 415
CONNECT option, 416
EXTEND= option, 416
GRIDSIZE= option, 416
ILINK option, 416
INDIVIDUAL option, 416
LIMITS option, 416
LINK option, 416
MOFF option, 416
NCOLS= option, 416
NOCLI option, 417
NOCLM option, 417
NOCLUSTER option, 417
NOCONNECT option, 417
NOLIMITS option, 417
NOOBS option, 417
NROWS= option, 417
OBS option, 417
PLOTBY= option, 420
PLOTBYLEN= option, 421
POLYBAR option, 421
PREDLABEL= option, 421
SHOWCLEGEND option, 421
SLICEBY= option, 421
SMOOTH option, 421
UNPACK option, 421
X= option, 421
Y= option, 422
YRANGE= option, 422
PLM procedure, ESTIMATE statement
ADJDFE= option, 440
ADJUST= option, 440
ALPHA= option, 441
CATEGORY= option, 441
CHISQ option, 442
CL option, 442
CORR option, 442
COV option, 442
DF= option, 442
DIVISOR= option, 442
E option, 443
EXP option, 443
ILINK option, 443
JOINT option, 444
LOWER option, 445
NOFILL option, 445
ODS graph names, 452
ODS table names, 452
PLOTS= option, 445
SEED= option, 446
SINGULAR= option, 446
STEPDOWN option, 446
TESTVALUE option, 448
UPPER option, 448
PLM procedure, LSMEANS statement
ADJDFE= option, 455
ADJUST= option, 456
ALPHA= option, 458
AT= option, 458
BYLEVEL option, 459
CL option, 459
CORR option, 459
COV option, 459
DF= option, 460
DIFF option, 460
E option, 461
EXP option, 461
ILINK option, 461
LINES option, 461
MEANS or NOMEANS option, 462
OBSMARGINS= option, 462
ODDSRATIO option, 462
ODS graph names, 468
ODS table names, 468
PDIFF option, 463
PLOTS= option, 463
SEED= option, 466
SINGULAR= option, 467
STEPDOWN option, 467
PLM procedure, LSMESIIMATE statement
ADJDFE= option, 472
ADJUST= option, 473
ALPHA= option, 473
AT= option, 473
BYLEVEL option, 473
CATEGORY= option, 473
CHISQ option, 474
CL option, 474
CORR option, 474
COV option, 474
DF= option, 474
DIVISOR= option, 474
E option, 475
ELSM option, 475
EXP option, 475
ILINK option, 475
JOINT option, 476
LOWER option, 477
OBSMARGINS= option, 477
ODS graph names, 481
ODS table names, 481
PLOTS= option, 477
SEED= option, 478
SINGULAR= option, 479
STEPDOWN option, 479
TESTVALUE= option, 480
UPPER option, 480
PLM procedure, SLICE statement
ADJDFE= option, 455
ADJUST= option, 456
ALPHA= option, 458
AT= option, 458
BYLEVEL option, 459
CL option, 459
CORR option, 459
COV option, 459
DF= option, 460
DIFF option, 460
E option, 461
EXP option, 461
ILINK option, 461
LINES option, 461
MEANS or NOMEANS option, 462
NOF option, 501
OBSMARGINS= option, 462
ODDSRATIO option, 462
ODS table names, 501
PDIFF option, 463
PLOTS= option, 463
SEED= option, 466
SIMPLE= option, 500
SINGULAR= option, 467
SLICEBY= option, 500
STEPDOWN option, 467
PLM procedure, TEST statement
CHISQ option, 503
DDF= option, 503
E option, 503
E1 option, 503
E2 option, 504
E3 option, 504
HTYPE= option, 504
INTERCEPT option, 504
ODS table names, 504
PLOTBY= option
EFFECTPLOT statement, 420
PLOTBYLEN= option
EFFECTPLOT statement, 421
PLOTS= option
ESTIMATE statement (LIFEREG), 445
ESTIMATE statement (PHREG), 445
ESTIMATE statement (PLM), 445
LSMEANS statement (GENMOD), 463
LSMEANS statement (LIFEREG), 463
LSMEANS statement (LOGISTIC), 463
LSMEANS statement (ORTHOREG), 463
LSMEANS statement (PHREG), 463
LSMEANS statement (PLM), 463
LSMEANS statement (PROBIT), 463
LSMEANS statement (SURVEYLOGISTIC),
463
LSMEANS statement (SURVEYPHREG), 463
LSMEANS statement (SURVEYREG), 463
LSMESTIMATE statement (GENMOD), 477
LSMESTIMATE statement (LIFEREG), 477
LSMESTIMATE statement (LOGISTIC), 477
LSMESTIMATE statement (MIXED), 477
LSMESTIMATE statement (ORTHOREG), 477
LSMESTIMATE statement (PHREG), 477
LSMESTIMATE statement (PLM), 477
LSMESTIMATE statement (PROBIT), 477
LSMESTIMATE statement
(SURVEYLOGISTIC), 477
LSMESTIMATE statement (SURVEYPHREG),
477
LSMESTIMATE statement (SURVEYREG),
477
SLICE statement (GENMOD), 463
SLICE statement (GLIMMIX), 463
SLICE statement (LIFEREG), 463
SLICE statement (LOGISTIC), 463
SLICE statement (MIXED), 463
SLICE statement (ORTHOREG), 463
SLICE statement (PHREG), 463
SLICE statement (PLM), 463
SLICE statement (PROBIT), 463
SLICE statement (SURVEYLOGISTIC), 463
SLICE statement (SURVEYPHREG), 463
SLICE statement (SURVEYREG), 463
PLS procedure, EFFECT statement
BASIS option (spline), 403
collection effect, 395
DATABOUNDARY option (spline), 404
DEGREE option (polynomial), 400
DEGREE option (spline), 404
DESIGNROLE option (lag), 397
DETAILS option (lag), 397
DETAILS option (multimember), 399
DETAILS option (polynomial), 400
DETAILS option (spline), 404
KNOTMAX option (spline), 404
KNOTMETHOD option (spline), 404
KNOTMIN option (spline), 406
LABELSTYLE option (polynomial), 400
lag effect, 395
MDEGREE option (polynomial), 401
multimember effect, 398
NATURALCUBIC option (spline), 406
NLAG option (lag), 398
NOEFFECT option (multimember), 399
NOSEPARATE option (polynomial), 401
PERIOD option (lag), 397
polynomial effect, 399
SEPARATE option (spline), 406
spline effect, 403
SPLIT option (spline), 406
STANDARDIZE option (polynomial), 401
WITHIN option (lag), 397
POLYBAR option
EFFECTPLOT statement, 421
PREDLABEL= option
EFFECTPLOT statement, 421
PROBIT procedure, ESTIMATE statement
ADJUST= option, 440
ALPHA= option, 441
CATEGORY= option, 441
CL option, 442
CORR option, 442
COV option, 442
DIVISOR= option, 442
E option, 443
EXP option, 443
ILINK option, 443
JOINT option, 444
LOWER option, 445
NOFILL option, 445
ODS table names, 452
SEED= option, 446
SINGULAR= option, 446
STEPDOWN option, 446
TESTVALUE option, 448
UPPER option, 448
PROBIT procedure, LSMEANS statement
ADJUST= option, 456
ALPHA= option, 458
AT= option, 458
BYLEVEL option, 459
CL option, 459
CORR option, 459
COV option, 459
DIFF option, 460
E option, 461
EXP option, 461
ILINK option, 461
LINES option, 461
MEANS or NOMEANS option, 462
OBSMARGINS= option, 462
ODDSRATIO option, 462
ODS graph names, 468
ODS table names, 468
PDIFF option, 463
PLOTS= option, 463
SEED= option, 466
SINGULAR= option, 467
STEPDOWN option, 467
PROBIT procedure, LSMESIIMATE statement
ADJUST= option, 473
ALPHA= option, 473
AT= option, 473
BYLEVEL option, 473
CATEGORY= option, 473
CL option, 474
COV option, 474
DIVISOR= option, 474
E option, 475
ELSM option, 475
ILINK option, 475
JOINT option, 476
LOWER option, 477
OBSMARGINS= option, 477
ODS table names, 481
PLOTS= option, 477
SEED= option, 478
SINGULAR= option, 479
STEPDOWN option, 479
TESTVALUE= option, 480
UPPER option, 480
PROBIT procedure, SLICE statement
ADJUST= option, 456
ALPHA= option, 458
AT= option, 458
BYLEVEL option, 459
CL option, 459
CORR option, 459
COV option, 459
DIFF option, 460
E option, 461
EXP option, 461
ILINK option, 461
LINES option, 461
MEANS or NOMEANS option, 462
NOF option, 501
OBSMARGINS= option, 462
ODS table names, 501
PDIFF option, 463
PLOTS= option, 463
SEED= option, 466
SIMPLE= option, 500
SINGULAR= option, 467
SLICEBY= option, 500
STEPDOWN option, 467
PROBIT procedure, TEST statement
CHISQ option, 503
DDF= option, 503
E option, 503
E1 option, 503
E2 option, 504
E3 option, 504
HTYPE= option, 504
INTERCEPT option, 504
ODS table names, 504
QUANTLIFE procedure, EFFECT statement
BASIS option (spline), 403
collection effect, 395
DATABOUNDARY option (spline), 404
DEGREE option (polynomial), 400
DEGREE option (spline), 404
DESIGNROLE option (lag), 397
DETAILS option (lag), 397
DETAILS option (multimember), 399
DETAILS option (polynomial), 400
DETAILS option (spline), 404
KNOTMAX option (spline), 404
KNOTMETHOD option (spline), 404
KNOTMIN option (spline), 406
LABELSTYLE option (polynomial), 400
lag effect, 395
MDEGREE option (polynomial), 401
multimember effect, 398
NLAG option (lag), 398
NOEFFECT option (multimember), 399
NOSEPARATE option (polynomial), 401
PERIOD option (lag), 397
polynomial effect, 399
SEPARATE option (spline), 406
spline effect, 403
SPLIT option (spline), 406
STANDARDIZE option (polynomial), 401
WITHIN option (lag), 397
QUANTREG procedure, EFFECT statement
BASIS option (spline), 403
collection effect, 395
DATABOUNDARY option (spline), 404
DEGREE option (polynomial), 400
DEGREE option (spline), 404
DESIGNROLE option (lag), 397
DETAILS option (lag), 397
DETAILS option (multimember), 399
DETAILS option (polynomial), 400
DETAILS option (spline), 404
KNOTMAX option (spline), 404
KNOTMETHOD option (spline), 404
KNOTMIN option (spline), 406
LABELSTYLE option (polynomial), 400
lag effect, 395
MDEGREE option (polynomial), 401
multimember effect, 398
NATURALCUBIC option (spline), 406
NLAG option (lag), 398
NOEFFECT option (multimember), 399
NOSEPARATE option (polynomial), 401
PERIOD option (lag), 397
polynomial effect, 399
SEPARATE option (spline), 406
spline effect, 403
SPLIT option (spline), 406
STANDARDIZE option (polynomial), 401
WITHIN option (lag), 397
QUANTREG procedure, ESTIMATE statement
ADJUST= option, 440
ALPHA= option, 441
CL option, 442
CORR option, 442
COV option, 442
DIVISOR= option, 442
E option, 443
JOINT option, 444
LOWER option, 445
NOFILL option, 445
ODS table names, 452
SEED= option, 446
SINGULAR= option, 446
STEPDOWN option, 446
TESTVALUE option, 448
UPPER option, 448
QUANTSELECT procedure, EFFECT statement
BASIS option (spline), 403
collection effect, 395
DATABOUNDARY option (spline), 404
DEGREE option (polynomial), 400
DEGREE option (spline), 404
DESIGNROLE option (lag), 397
DETAILS option (lag), 397
DETAILS option (multimember), 399
DETAILS option (polynomial), 400
DETAILS option (spline), 404
KNOTMAX option (spline), 404
KNOTMETHOD option (spline), 404
KNOTMIN option (spline), 406
LABELSTYLE option (polynomial), 400
lag effect, 395
MDEGREE option (polynomial), 401
multimember effect, 398
NLAG option (lag), 398
NOEFFECT option (multimember), 399
NOSEPARATE option (polynomial), 401
PERIOD option (lag), 397
polynomial effect, 399
SEPARATE option (spline), 406
spline effect, 403
SPLIT option (spline), 406
STANDARDIZE option (polynomial), 401
WITHIN option (lag), 397
REG procedure, CODE statement
CATALOG= option, 391
DUMMIES option, 391
ERRORS option, 392
FILE= option, 392
FORMAT= option, 392
GROUP= option, 392
IMPUTE option, 392
LINESIZE= option, 392
LOOKUP= option, 392
NODUMMIES option, 391
NOERRORS option, 392
NORESIDUAL option, 393
RESIDUAL option, 393
RESIDUAL option
CODE statement (GENMOD), 393
CODE statement (GLIMMIX), 393
CODE statement (GLM), 393
CODE statement (GLMSELECT), 393
CODE statement (LOGISTIC), 393
CODE statement (PLM), 393
CODE statement (REG), 393
REST option
NLOPTIONS statement (CALIS), 491
NLOPTIONS statement (GLIMMIX), 491
NLOPTIONS statement (HPMIXED), 491
NLOPTIONS statement (PHREG), 491
NLOPTIONS statement (SURVEYPHREG), 491
NLOPTIONS statement (VARIOGRAM), 491
RESTART option
NLOPTIONS statement (CALIS), 491
NLOPTIONS statement (GLIMMIX), 491
NLOPTIONS statement (HPMIXED), 491
NLOPTIONS statement (PHREG), 491
NLOPTIONS statement (SURVEYPHREG), 491
NLOPTIONS statement (VARIOGRAM), 491
ROBUSTREG procedure, EFFECT statement
BASIS option (spline), 403
collection effect, 395
DATABOUNDARY option (spline), 404
DEGREE option (polynomial), 400
DEGREE option (spline), 404
DESIGNROLE option (lag), 397
DETAILS option (lag), 397
DETAILS option (multimember), 399
DETAILS option (polynomial), 400
DETAILS option (spline), 404
KNOTMAX option (spline), 404
KNOTMETHOD option (spline), 404
KNOTMIN option (spline), 406
LABELSTYLE option (polynomial), 400
lag effect, 395
MDEGREE option (polynomial), 401
multimember effect, 398
NATURALCUBIC option (spline), 406
NLAG option (lag), 398
NOEFFECT option (multimember), 399
NOSEPARATE option (polynomial), 401
PERIOD option (lag), 397
polynomial effect, 399
SEPARATE option (spline), 406
spline effect, 403
SPLIT option (spline), 406
STANDARDIZE option (polynomial), 401
WITHIN option (lag), 397
SEED= option
ESTIMATE statement (LIFEREG), 446
ESTIMATE statement (LOGISTIC), 446
ESTIMATE statement (ORTHOREG), 446
ESTIMATE statement (PHREG), 446
ESTIMATE statement (PLM), 446
ESTIMATE statement (PROBIT), 446
ESTIMATE statement (QUANTREG), 446
ESTIMATE statement (SURVEYLOGISTIC),
446
ESTIMATE statement (SURVEYPHREG), 446
ESTIMATE statement (SURVEYREG), 446
LSMEANS statement (GENMOD), 466
LSMEANS statement (LIFEREG), 466
LSMEANS statement (LOGISTIC), 466
LSMEANS statement (ORTHOREG), 466
LSMEANS statement (PHREG), 466
LSMEANS statement (PLM), 466
LSMEANS statement (PROBIT), 466
LSMEANS statement (SURVEYLOGISTIC),
466
LSMEANS statement (SURVEYPHREG), 466
LSMEANS statement (SURVEYREG), 466
LSMESTIMATE statement (GENMOD), 478
LSMESTIMATE statement (LIFEREG), 478
LSMESTIMATE statement (LOGISTIC), 478
LSMESTIMATE statement (MIXED), 478
LSMESTIMATE statement (ORTHOREG), 478
LSMESTIMATE statement (PHREG), 478
LSMESTIMATE statement (PLM), 478
LSMESTIMATE statement (PROBIT), 478
LSMESTIMATE statement
(SURVEYLOGISTIC), 478
LSMESTIMATE statement (SURVEYPHREG),
478
LSMESTIMATE statement (SURVEYREG),
478
SLICE statement (GENMOD), 466
SLICE statement (GLIMMIX), 466
SLICE statement (LIFEREG), 466
SLICE statement (LOGISTIC), 466
SLICE statement (MIXED), 466
SLICE statement (ORTHOREG), 466
SLICE statement (PHREG), 466
SLICE statement (PLM), 466
SLICE statement (PROBIT), 466
SLICE statement (SURVEYLOGISTIC), 466
SLICE statement (SURVEYPHREG), 466
SLICE statement (SURVEYREG), 466
SEPARATE option
EFFECT statement, spline (GLIMMIX), 406
EFFECT statement, spline (GLMSELECT), 406
EFFECT statement, spline (HPMIXED), 406
EFFECT statement, spline (LOGISTIC), 406
EFFECT statement, spline (ORTHOREG), 406
EFFECT statement, spline (PHREG), 406
EFFECT statement, spline (PLS), 406
EFFECT statement, spline (QUANTLIFE), 406
EFFECT statement, spline (QUANTREG), 406
EFFECT statement, spline (QUANTSELECT),
406
EFFECT statement, spline (ROBUSTREG), 406
EFFECT statement, spline
(SURVEYLOGISTIC), 406
EFFECT statement, spline (SURVEYREG), 406
SHOWCLEGEND option
EFFECTPLOT statement, 421
SIMPLE= option
SLICE statement (GENMOD), 500
SLICE statement (GLIMMIX), 500
SLICE statement (LIFEREG), 500
SLICE statement (LOGISTIC), 500
SLICE statement (MIXED), 500
SLICE statement (ORTHOREG), 500
SLICE statement (PHREG), 500
SLICE statement (PLM), 500
SLICE statement (PROBIT), 500
SLICE statement (SURVEYLOGISTIC), 500
SLICE statement (SURVEYPHREG), 500
SLICE statement (SURVEYREG), 500
SINGULAR= option
ESTIMATE statement (LIFEREG), 446
ESTIMATE statement (LOGISTIC), 446
ESTIMATE statement (ORTHOREG), 446
ESTIMATE statement (PHREG), 446
ESTIMATE statement (PLM), 446
ESTIMATE statement (PROBIT), 446
ESTIMATE statement (QUANTREG), 446
ESTIMATE statement (SURVEYLOGISTIC),
446
ESTIMATE statement (SURVEYPHREG), 446
ESTIMATE statement (SURVEYREG), 446
LSMEANS statement (GENMOD), 467
LSMEANS statement (LIFEREG), 467
LSMEANS statement (LOGISTIC), 467
LSMEANS statement (ORTHOREG), 467
LSMEANS statement (PHREG), 467
LSMEANS statement (PLM), 467
LSMEANS statement (PROBIT), 467
LSMEANS statement (SURVEYLOGISTIC),
467
LSMEANS statement (SURVEYPHREG), 467
LSMEANS statement (SURVEYREG), 467
LSMESTIMATE statement (GENMOD), 479
LSMESTIMATE statement (LIFEREG), 479
LSMESTIMATE statement (LOGISTIC), 479
LSMESTIMATE statement (MIXED), 479
LSMESTIMATE statement (ORTHOREG), 479
LSMESTIMATE statement (PHREG), 479
LSMESTIMATE statement (PLM), 479
LSMESTIMATE statement (PROBIT), 479
LSMESTIMATE statement
(SURVEYLOGISTIC), 479
LSMESTIMATE statement (SURVEYPHREG),
479
LSMESTIMATE statement (SURVEYREG),
479
NLOPTIONS statement (CALIS), 492
NLOPTIONS statement (GLIMMIX), 492
NLOPTIONS statement (HPMIXED), 492
NLOPTIONS statement (PHREG), 492
NLOPTIONS statement (SURVEYPHREG), 492
NLOPTIONS statement (VARIOGRAM), 492
SLICE statement (GENMOD), 467
SLICE statement (GLIMMIX), 467
SLICE statement (LIFEREG), 467
SLICE statement (LOGISTIC), 467
SLICE statement (MIXED), 467
SLICE statement (ORTHOREG), 467
SLICE statement (PHREG), 467
SLICE statement (PLM), 467
SLICE statement (PROBIT), 467
SLICE statement (SURVEYLOGISTIC), 467
SLICE statement (SURVEYPHREG), 467
SLICE statement (SURVEYREG), 467
SLICE statement
GENMOD procedure, 498
GLIMMIX procedure, 498
LIFEREG procedure, 498
LOGISTIC procedure, 498
MIXED procedure, 498
ORTHOREG procedure, 498
PHREG procedure, 498
PLM procedure, 498
PROBIT procedure, 498
SURVEYLOGISTIC procedure, 498
SURVEYPHREG procedure, 498
SURVEYREG procedure, 498
SLICEBY= option
EFFECTPLOT statement, 421
SLICE statement (GENMOD), 500
SLICE statement (GLIMMIX), 500
SLICE statement (LIFEREG), 500
SLICE statement (LOGISTIC), 500
SLICE statement (MIXED), 500
SLICE statement (ORTHOREG), 500
SLICE statement (PHREG), 500
SLICE statement (PLM), 500
SLICE statement (PROBIT), 500
SLICE statement (SURVEYLOGISTIC), 500
SLICE statement (SURVEYPHREG), 500
SLICE statement (SURVEYREG), 500
SMOOTH option
EFFECTPLOT statement, 421
SOCKET option
NLOPTIONS statement (CALIS), 492
NLOPTIONS statement (GLIMMIX), 492
NLOPTIONS statement (HPMIXED), 492
NLOPTIONS statement (PHREG), 492
NLOPTIONS statement (SURVEYPHREG), 492
NLOPTIONS statement (VARIOGRAM), 492
SPLIT option
EFFECT statement, spline (GLMSELECT), 406
EFFECT statement, spline (HPMIXED), 406
EFFECT statement, spline (LOGISTIC), 406
EFFECT statement, spline (ORTHOREG), 406
EFFECT statement, spline (PHREG), 406
EFFECT statement, spline (PLS), 406
EFFECT statement, spline (QUANTLIFE), 406
EFFECT statement, spline (QUANTREG), 406
EFFECT statement, spline (QUANTSELECT),
406
EFFECT statement, spline (ROBUSTREG), 406
EFFECT statement, spline
(SURVEYLOGISTIC), 406
EFFECT statement, spline (SURVEYREG), 406
SRUVEYPHREG procedure, NLOPTIONS statement
ABSCONV option, 484
STANDARDIZE option
EFFECT statement, polynomial (GLIMMIX),
401
EFFECT statement, polynomial
(GLMSELECT), 401
EFFECT statement, polynomial (HPMIXED),
401
EFFECT statement, polynomial (LOGISTIC),
401
EFFECT statement, polynomial (ORTHOREG),
401
EFFECT statement, polynomial (PHREG), 401
EFFECT statement, polynomial (PLS), 401
EFFECT statement, polynomial (QUANTLIFE),
401
EFFECT statement, polynomial (QUANTREG),
401
EFFECT statement, polynomial
(QUANTSELECT), 401
EFFECT statement, polynomial
(ROBUSTREG), 401
EFFECT statement, polynomial
(SURVEYLOGISTIC), 401
EFFECT statement, polynomial
(SURVEYREG), 401
STEPDOWN option
ESTIMATE statement (LIFEREG), 446
ESTIMATE statement (LOGISTIC), 446
ESTIMATE statement (ORTHOREG), 446
ESTIMATE statement (PHREG), 446
ESTIMATE statement (PLM), 446
ESTIMATE statement (PROBIT), 446
ESTIMATE statement (QUANTREG), 446
ESTIMATE statement (SURVEYLOGISTIC),
446
ESTIMATE statement (SURVEYPHREG), 446
ESTIMATE statement (SURVEYREG), 446
LSMEANS statement (GENMOD), 467
LSMEANS statement (LIFEREG), 467
LSMEANS statement (LOGISTIC), 467
LSMEANS statement (ORTHOREG), 467
LSMEANS statement (PHREG), 467
LSMEANS statement (PLM), 467
LSMEANS statement (PROBIT), 467
LSMEANS statement (SURVEYLOGISTIC),
467
LSMEANS statement (SURVEYPHREG), 467
LSMEANS statement (SURVEYREG), 467
LSMESTIMATE statement (GENMOD), 479
LSMESTIMATE statement (LIFEREG), 479
LSMESTIMATE statement (LOGISTIC), 479
LSMESTIMATE statement (MIXED), 479
LSMESTIMATE statement (ORTHOREG), 479
LSMESTIMATE statement (PHREG), 479
LSMESTIMATE statement (PLM), 479
LSMESTIMATE statement (PROBIT), 479
LSMESTIMATE statement
(SURVEYLOGISTIC), 479
LSMESTIMATE statement (SURVEYPHREG),
479
LSMESTIMATE statement (SURVEYREG),
479
SLICE statement (GENMOD), 467
SLICE statement (GLIMMIX), 467
SLICE statement (LIFEREG), 467
SLICE statement (LOGISTIC), 467
SLICE statement (MIXED), 467
SLICE statement (ORTHOREG), 467
SLICE statement (PHREG), 467
SLICE statement (PLM), 467
SLICE statement (PROBIT), 467
SLICE statement (SURVEYLOGISTIC), 467
SLICE statement (SURVEYPHREG), 467
SLICE statement (SURVEYREG), 467
STORE statement
GENMOD procedure, 501
GLIMMIX procedure, 501
GLM procedure, 501
GLMSELECT procedure, 501
LIFEREG procedure, 501
LOGISTIC procedure, 501
MIXED procedure, 501
ORTHOREG procedure, 501
PHREG procedure, 501
PROBIT procedure, 501
SURVEYLOGISTIC procedure, 501
SURVEYPHREG procedure, 501
SURVEYREG procedure, 501
SUREYREG procedure, EFFECT statement
DESIGNROLE option (lag), 397
SURVEYLOGISTIC procedure, EFFECT statement
BASIS option (spline), 403
collection effect, 395
DATABOUNDARY option (spline), 404
DEGREE option (polynomial), 400
DEGREE option (spline), 404
DESIGNROLE option (lag), 397
DETAILS option (lag), 397
DETAILS option (multimember), 399
DETAILS option (polynomial), 400
DETAILS option (spline), 404
KNOTMAX option (spline), 404
KNOTMETHOD option (spline), 404
KNOTMIN option (spline), 406
LABELSTYLE option (polynomial), 400
lag effect, 395
MDEGREE option (polynomial), 401
multimember effect, 398
NATURALCUBIC option (spline), 406
NLAG option (lag), 398
NOEFFECT option (multimember), 399
NOSEPARATE option (polynomial), 401
PERIOD option (lag), 397
polynomial effect, 399
SEPARATE option (spline), 406
spline effect, 403
SPLIT option (spline), 406
STANDARDIZE option (polynomial), 401
WITHIN option (lag), 397
SURVEYLOGISTIC procedure, ESTIMATE
statement
ADJUST= option, 440
ALPHA= option, 441
CATEGORY= option, 441
CL option, 442
CORR option, 442
COV option, 442
DIVISOR= option, 442
E option, 443
EXP option, 443
ILINK option, 443
JOINT option, 444
LOWER option, 445
NOFILL option, 445
ODS table names, 452
SEED= option, 446
SINGULAR= option, 446
STEPDOWN option, 446
TESTVALUE option, 448
UPPER option, 448
SURVEYLOGISTIC procedure, LSMEANS
statement
ADJUST= option, 456
ALPHA= option, 458
AT= option, 458
BYLEVEL option, 459
CL option, 459
CORR option, 459
COV option, 459
DIFF option, 460
E option, 461
EXP option, 461
ILINK option, 461
LINES option, 461
MEANS or NOMEANS option, 462
OBSMARGINS= option, 462
ODDSRATIO option, 462
ODS graph names, 468
ODS table names, 468
PDIFF option, 463
PLOTS= option, 463
SEED= option, 466
SINGULAR= option, 467
STEPDOWN option, 467
SURVEYLOGISTIC procedure, LSMESIIMATE
statement
ADJUST= option, 473
ALPHA= option, 473
AT= option, 473
BYLEVEL option, 473
CATEGORY= option, 473
CL option, 474
CORR option, 474
COV option, 474
DIVISOR= option, 474
E option, 475
ELSM option, 475
EXP option, 475
ILINK option, 475
JOINT option, 476
LOWER option, 477
OBSMARGINS= option, 477
ODS table names, 481
PLOTS= option, 477
SEED= option, 478
SINGULAR= option, 479
STEPDOWN option, 479
TESTVALUE= option, 480
UPPER option, 480
SURVEYLOGISTIC procedure, SLICE statement
ADJUST= option, 456
ALPHA= option, 458
AT= option, 458
BYLEVEL option, 459
CL option, 459
CORR option, 459
COV option, 459
DIFF option, 460
E option, 461
EXP option, 461
ILINK option, 461
LINES option, 461
MEANS or NOMEANS option, 462
NOF option, 501
OBSMARGINS= option, 462
ODDSRATIO option, 462
ODS table names, 501
PDIFF option, 463
PLOTS= option, 463
SEED= option, 466
SIMPLE= option, 500
SINGULAR= option, 467
SLICEBY= option, 500
STEPDOWN option, 467
SURVEYPHREG procedure, ESTIMATE statement
ADJDFE= option, 440
ADJUST= option, 440
ALPHA= option, 441
CHISQ option, 442
CL option, 442
CORR option, 442
COV option, 442
DF= option, 442
DIVISOR= option, 442
E option, 443
JOINT option, 444
LOWER option, 445
NOFILL option, 445
ODS table names, 452
SEED= option, 446
SINGULAR= option, 446
STEPDOWN option, 446
TESTVALUE option, 448
UPPER option, 448
SURVEYPHREG procedure, LSMEANS statement
ADJDFE= option, 455
ADJUST= option, 456
ALPHA= option, 458
AT= option, 458
BYLEVEL option, 459
CL option, 459
CORR option, 459
COV option, 459
DF= option, 460
DIFF option, 460
E option, 461
LINES option, 461
MEANS or NOMEANS option, 462
OBSMARGINS= option, 462
ODS graph names, 468
ODS table names, 468
PDIFF option, 463
PLOTS= option, 463
SEED= option, 466
SINGULAR= option, 467
STEPDOWN option, 467
SURVEYPHREG procedure, LSMESIIMATE
statement
ADJDFE= option, 472
ADJUST= option, 473
ALPHA= option, 473
AT= option, 473
BYLEVEL option, 473
CHISQ option, 474
CL option, 474
CORR option, 474
COV option, 474
DF= option, 474
DIVISOR= option, 474
E option, 475
ELSM option, 475
JOINT option, 476
LOWER option, 477
OBSMARGINS= option, 477
ODS table names, 481
PLOTS= option, 477
SEED= option, 478
SINGULAR= option, 479
STEPDOWN option, 479
TESTVALUE= option, 480
UPPER option, 480
SURVEYPHREG procedure, NLOPTIONS statement
ABSFCONV option, 484
ABSGCONV option, 484
ABSGTOL option, 484
ABSTOL option, 484
ABSXCONV option, 484
ABSXTOL option, 484
ASINGULAR= option, 485
FCONV option, 485
FCONV2 option, 486
FSIZE option, 486
FTOL option, 485
FTOL2 option, 486
GCONV option, 486
GCONV2 option, 487
GTOL option, 486
GTOL2 option, 487
HESCAL option, 487
HS option, 487
INHESSIAN option, 488
INSTEP option, 488
LCDEACT= option, 488
LCEPSILON= option, 489
LCSINGULAR= option, 489
LINESEARCH option, 489
LSP option, 490
LSPRECISION option, 490
MAXFU option, 490
MAXFUNC option, 490
MAXIT option, 490
MAXITER option, 490
MAXSTEP option, 491
MAXTIME option, 491
MINIT option, 491
MINITER option, 491
MSINGULAR= option, 491
REST option, 491
RESTART option, 491
SINGULAR= option, 492
SOCKET option, 492
TECH option, 492
TECHNIQUE option, 492
UPD option, 493
VSINGULAR= option, 494
XSIZE option, 494
XTOL option, 494
SURVEYPHREG procedure, SLICE statement
ADJUST= option, 456
ALPHA= option, 458
AT= option, 458
BYLEVEL option, 459
CL option, 459
CORR option, 459
COV option, 459
DF= option, 460
DIFF option, 460
E option, 461
LINES option, 461
MEANS or NOMEANS option, 462
NOF option, 501
OBSMARGINS= option, 462
ODS table names, 501
PDIFF option, 463
PLOTS= option, 463
SEED= option, 466
SIMPLE= option, 500
SINGULAR= option, 467
SLICEBY= option, 500
STEPDOWN option, 467
SURVEYPHREG procedure, TEST statement
CHISQ option, 503
DDF= option, 503
E option, 503
E1 option, 503
E2 option, 504
E3 option, 504
HTYPE= option, 504
INTERCEPT option, 504
ODS table names, 504
SURVEYREG procedure, EFFECT statement
BASIS option (spline), 403
collection effect, 395
DATABOUNDARY option (spline), 404
DEGREE option (polynomial), 400
DEGREE option (spline), 404
DETAILS option (lag), 397
DETAILS option (multimember), 399
DETAILS option (polynomial), 400
DETAILS option (spline), 404
KNOTMAX option (spline), 404
KNOTMETHOD option (spline), 404
KNOTMIN option (spline), 406
LABELSTYLE option (polynomial), 400
lag effect, 395
MDEGREE option (polynomial), 401
multimember effect, 398
NATURALCUBIC option (spline), 406
NLAG option (lag), 398
NOEFFECT option (multimember), 399
NOSEPARATE option (polynomial), 401
PERIOD option (lag), 397
polynomial effect, 399
SEPARATE option (spline), 406
spline effect, 403
SPLIT option (spline), 406
STANDARDIZE option (polynomial), 401
WITHIN option (lag), 397
SURVEYREG procedure, ESTIMATE statement
ADJDFE= option, 440
ADJUST= option, 440
ALPHA= option, 441
CHISQ option, 442
CL option, 442
CORR option, 442
COV option, 442
DF= option, 442
DIVISOR= option, 442
E option, 443
JOINT option, 444
LOWER option, 445
NOFILL option, 445
ODS table names, 452
SEED= option, 446
SINGULAR= option, 446
STEPDOWN option, 446
TESTVALUE option, 448
UPPER option, 448
SURVEYREG procedure, LSMEANS statement
ADJDFE= option, 455
ADJUST= option, 456
ALPHA= option, 458
AT= option, 458
BYLEVEL option, 459
CL option, 459
CORR option, 459
COV option, 459
DF= option, 460
DIFF option, 460
E option, 461
LINES option, 461
MEANS or NOMEANS option, 462
OBSMARGINS= option, 462
ODS graph names, 468
ODS table names, 468
PDIFF option, 463
PLOTS= option, 463
SEED= option, 466
SINGULAR= option, 467
STEPDOWN option, 467
SURVEYREG procedure, LSMESIIMATE statement
ADJDFE= option, 472
ADJUST= option, 473
ALPHA= option, 473
AT= option, 473
BYLEVEL option, 473
CHISQ option, 474
CL option, 474
CORR option, 474
COV option, 474
DF= option, 474
DIVISOR= option, 474
E option, 475
ELSM option, 475
JOINT option, 476
LOWER option, 477
OBSMARGINS= option, 477
ODS table names, 481
PLOTS= option, 477
SEED= option, 478
SINGULAR= option, 479
STEPDOWN option, 479
TESTVALUE= option, 480
UPPER option, 480
SURVEYREG procedure, SLICE statement
ADJUST= option, 456
ALPHA= option, 458
AT= option, 458
BYLEVEL option, 459
CL option, 459
CORR option, 459
COV option, 459
DF= option, 460
DIFF option, 460
E option, 461
LINES option, 461
MEANS or NOMEANS option, 462
NOF option, 501
OBSMARGINS= option, 462
ODS table names, 501
PDIFF option, 463
PLOTS= option, 463
SEED= option, 466
SIMPLE= option, 500
SINGULAR= option, 467
SLICEBY= option, 500
STEPDOWN option, 467
SURVEYREG procedure, TEST statement
CHISQ option, 503
DDF= option, 503
E option, 503
E1 option, 503
E2 option, 504
E3 option, 504
HTYPE= option, 504
INTERCEPT option, 504
ODS table names, 504
TECH option
NLOPTIONS statement (CALIS), 492
NLOPTIONS statement (GLIMMIX), 492
NLOPTIONS statement (HPMIXED), 492
NLOPTIONS statement (PHREG), 492
NLOPTIONS statement (SURVEYPHREG), 492
NLOPTIONS statement (VARIOGRAM), 492
TECHNIQUE option
NLOPTIONS statement (CALIS), 492
NLOPTIONS statement (GLIMMIX), 492
NLOPTIONS statement (HPMIXED), 492
NLOPTIONS statement (PHREG), 492
NLOPTIONS statement (SURVEYPHREG), 492
NLOPTIONS statement (VARIOGRAM), 492
TEST statement
LIFEREG procedure, 502
ORTHOREG procedure, 502
PLM procedure, 502
PROBIT procedure, 502
SURVEYPHREG procedure, 502
SURVEYREG procedure, 502
TESTVALUE= option
ESTIMATE statement (LIFEREG), 448
ESTIMATE statement (LOGISTIC), 448
ESTIMATE statement (ORTHOREG), 448
ESTIMATE statement (PHREG), 448
ESTIMATE statement (PLM), 448
ESTIMATE statement (PROBIT), 448
ESTIMATE statement (QUANTREG), 448
ESTIMATE statement (SURVEYLOGISTIC),
448
ESTIMATE statement (SURVEYPHREG), 448
ESTIMATE statement (SURVEYREG), 448
LSMESTIMATE statement (GENMOD), 480
LSMESTIMATE statement (LIFEREG), 480
LSMESTIMATE statement (LOGISTIC), 480
LSMESTIMATE statement (MIXED), 480
LSMESTIMATE statement (ORTHOREG), 480
LSMESTIMATE statement (PHREG), 480
LSMESTIMATE statement (PLM), 480
LSMESTIMATE statement (PROBIT), 480
LSMESTIMATE statement
(SURVEYLOGISTIC), 480
LSMESTIMATE statement (SURVEYPHREG),
480
LSMESTIMATE statement (SURVEYREG),
480
UNPACK option
EFFECTPLOT statement, 421
UPD option
NLOPTIONS statement (CALIS), 493
NLOPTIONS statement (GLIMMIX), 493
NLOPTIONS statement (HPMIXED), 493
NLOPTIONS statement (PHREG), 493
NLOPTIONS statement (SURVEYPHREG), 493
NLOPTIONS statement (VARIOGRAM), 493
UPDATE option
NLOPTIONS statement (CALIS), 493
NLOPTIONS statement (GLIMMIX), 493
NLOPTIONS statement (HPMIXED), 493
NLOPTIONS statement (PHREG), 493
NLOPTIONS statement (SURVEYPHREG), 493
NLOPTIONS statement (VARIOGRAM), 493
UPPER option
ESTIMATE statement (LIFEREG), 448
ESTIMATE statement (LOGISTIC), 448
ESTIMATE statement (ORTHOREG), 448
ESTIMATE statement (PHREG), 448
ESTIMATE statement (PLM), 448
ESTIMATE statement (PROBIT), 448
ESTIMATE statement (QUANTREG), 448
ESTIMATE statement (SURVEYLOGISTIC),
448
ESTIMATE statement (SURVEYPHREG), 448
ESTIMATE statement (SURVEYREG), 448
LSMESTIMATE statement (GENMOD), 480
LSMESTIMATE statement (LIFEREG), 480
LSMESTIMATE statement (LOGISTIC), 480
LSMESTIMATE statement (MIXED), 480
LSMESTIMATE statement (ORTHOREG), 480
LSMESTIMATE statement (PHREG), 480
LSMESTIMATE statement (PLM), 480
LSMESTIMATE statement (PROBIT), 480
LSMESTIMATE statement
(SURVEYLOGISTIC), 480
LSMESTIMATE statement (SURVEYPHREG),
480
LSMESTIMATE statement (SURVEYREG),
480
VARIOGRAM procedure, NLOPTIONS statement
ABSCONV option, 484
ABSFCONV option, 484
ABSGCONV option, 484
ABSGTOL option, 484
ABSTOL option, 484
ABSXCONV option, 484
ABSXTOL option, 484
ASINGULAR= option, 485
FCONV option, 485
FCONV2 option, 486
FSIZE option, 486
FTOL option, 485
FTOL2 option, 486
GCONV option, 486
GCONV2 option, 487
GTOL option, 486
GTOL2 option, 487
HESCAL option, 487
HS option, 487
INHESSIAN option, 488
INSTEP option, 488
LCDEACT= option, 488
LCEPSILON= option, 489
LCSINGULAR= option, 489
LINESEARCH option, 489
LSPRECISION option, 490
MAXFU option, 490
MAXFUNC option, 490
MAXIT option, 490
MAXITER option, 490
MAXSTEP option, 491
MAXTIME option, 491
MINIT option, 491
MINITER option, 491
MSINGULAR= option, 491
REST option, 491
RESTART option, 491
SINGULAR= option, 492
SOCKET option, 492
TECH option, 492
TECHNIQUE option, 492
UPD option, 493
VSINGULAR= option, 494
XSIZE option, 494
XTOL option, 494
VARIOGRAMprocedure, NLOPTIONS statement
LSP option, 490
VSINGULAR= option
NLOPTIONS statement (CALIS), 494
NLOPTIONS statement (GLIMMIX), 494
NLOPTIONS statement (HPMIXED), 494
NLOPTIONS statement (PHREG), 494
NLOPTIONS statement (SURVEYPHREG), 494
NLOPTIONS statement (VARIOGRAM), 494
WITHIN option
EFFECT statement, lag (GLIMMIX), 397
EFFECT statement, lag (GLMSELECT), 397
EFFECT statement, lag (HPMIXED), 397
EFFECT statement, lag (LOGISTIC), 397
EFFECT statement, lag (ORTHOREG), 397
EFFECT statement, lag (PHREG), 397
EFFECT statement, lag (PLS), 397
EFFECT statement, lag (QUANTLIFE), 397
EFFECT statement, lag (QUANTREG), 397
EFFECT statement, lag (QUANTSELECT), 397
EFFECT statement, lag (ROBUSTREG), 397
EFFECT statement, lag (SURVEYLOGISTIC),
397
EFFECT statement, lag (SURVEYREG), 397
X= option
EFFECTPLOT statement, 421
XCONV option
NLOPTIONS statement (CALIS), 494
NLOPTIONS statement (GLIMMIX), 494
NLOPTIONS statement (HPMIXED), 494
NLOPTIONS statement (PHREG), 494
NLOPTIONS statement (SURVEYPHREG), 494
NLOPTIONS statement (VARIOGRAM), 494
XSIZE option
NLOPTIONS statement (CALIS), 494
NLOPTIONS statement (GLIMMIX), 494
NLOPTIONS statement (HPMIXED), 494
NLOPTIONS statement (PHREG), 494
NLOPTIONS statement (SURVEYPHREG), 494
NLOPTIONS statement (VARIOGRAM), 494
XTOL option
NLOPTIONS statement (CALIS), 494
NLOPTIONS statement (GLIMMIX), 494
NLOPTIONS statement (HPMIXED), 494
NLOPTIONS statement (PHREG), 494
NLOPTIONS statement (SURVEYPHREG), 494
NLOPTIONS statement (VARIOGRAM), 494
Y= option
EFFECTPLOT statement, 422
YRANGE= option
EFFECTPLOT statement, 422
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