User`s Manual: WinGen2

User`s Manual: WinGen2
2011
User’s Manual:
SimulCAT
Kyung (Chris) T. Han
User’s Manual for SimulCAT 1
Header: User’s Manual: SimulCAT
User’s Manual for SimulCAT:
Windows Software for Simulating Computerized Adaptive Test Administration
Kyung T. Han
Graduate Management Admission Council ®
The views and opinions expressed in this article are those of the author and do not necessarily
reflect those of the Graduate Management Admission Council®.
User’s Manual for SimulCAT 2
I. Introduction
Most, if not all, computerized adaptive testing (CAT) programs use simulation techniques to
develop and evaluate CAT program administration and operations, but such simulation tools are
rarely available to the public. Up to now, several software tools have been available to conduct
CAT simulations for research purposes; however, these existing tools, for the most part,
oversimplify the CAT algorithms and are not powerful enough to simulate operational CAT
environments. SimulCAT, a new CAT simulation software tool, was developed to serve various
purposes ranging from fundamental CAT research to technical CAT program evaluations. The
new CAT simulation software tool offers many advantages, including a wide range of item
selection algorithms, adaptability for a variety of CAT administration environments, and a userfriendly graphical interface, among others, as described in the following commentary.
SimulCAT offers a variety of item selection algorithms.
The most widely used item selection algorithms—including maximized Fisher information (MFI;
Weiss, 1982), a-stratification (Chang & Ying, 1999; Chang, Qian, & Ying, 2001), global
information (Chang & Ying, 1996), interval information, likelihood weighted information
(Veerkamp & Berger, 1997), gradual maximum information ratio (GMIR; Han, 2009), and
efficiency balanced information (EBI; Han, 2010)—are available within. Along with a choice of
item selection criteria, a variety of item exposure control options are available within SimulCAT,
including, the randomesque strategy (Kingsbury & Zara, 1989), Sympson and Hetter method
(1985), the multinomial methods—both conditional and unconditional (Stocking & Lewis, 1995,
1998)—and the fade-away method (FAM; Han, 2009). For content balancing, SimulCAT
supports the content script method and the constrained CAT method (Kingsbury & Zara, 1989).
SimulCAT simulates various CAT environments.
To create CAT environments that are as realistic as possible, SimulCAT supports various CAT
administration options. First, the interim and final score estimates can be accomplished using the
maximum likelihood (ML), Bayesian maximum a posteriori (MAP), Bayes expected a posteriori
(EAP) estimations, or any combination of those. Software users also can set the initial score
value, range of score estimates, and restriction in estimate change. The length of CAT
administration can be either fixed or variable; for variable-length testing, SimulCAT supports
multiple termination rules including standard error of estimation and score estimate consistency.
Within SimulCAT, the number of test takers who are administered simultaneously at each test
time slot and the frequency of communication between a test server and client computers (i.e.,
terminals) can also be conditioned according to the user’s choice.
SimulCAT provides powerful research tools.
SimulCAT can read user-specified existing data and can generate new data sets as well. Score
distribution can be drawn from a normal, uniform, or beta distribution, and item parameters for
an item pool can be generated from normal, uniform, and/or lognormal distributions. The
SimulCAT tool also offers several graphical analysis tools such as distribution density functions,
User’s Manual for SimulCAT 3
item response functions, and information functions at both item and pool levels. SimulCAT can
generate reports on item pool usage and CAT administrations. For more advanced research,
SimulCAT provides users with options to input differential item functioning (DIF) or item
parameter drift (IPD) information as well as preexisting item exposure data. The software tool
also supports the use of syntax files and a cue file for massive simulation studies.
SimulCAT has an intuitive graphical user interface.
As a Windows-based application, SimulCAT provides a user-friendly graphical interface. Most
features of SimulCAT can be accessed by just a few simple point-and-clicks. The main interface
of SimulCAT consists of easy-to-follow three steps: Examinee/Item Data, Item Selection, and
Test Administration.
System Requirements, Availability, and Distribution
SimulCAT runs on a Microsoft Windows-based operating system with .NET framework 2.0 or
above. Microsoft’s Windows Vista and Windows 7 include .NET framework, but a machine
running an older version of the Windows OS will need to have .NET framework installed first.
The software package, a copy of the manual in PDF format, and example files can be found and
downloaded at the following web site: http://www.hantest.net. The software package is free of
charge and may be distributed to others without the author’s permission for noncommercial uses
only. SimulCAT always checks for the latest version and automatically updates itself as long as it
is running on a machine with an active Internet connection.
User’s Manual for SimulCAT 4
II. Item Selection Algorithms Used Within SimulCAT
SimulCAT supports nine item selection algorithm/criteria as follows:
1) Maximum Fisher Information (MFI)
2) a-Stratification (with/without b-blocking)
3) Best matching b-value
4) Randomization
5) Interval Information Criterion
6) Likelihood Information Criterion
7) Kullbak-Leibler Information (Global Information)
8) Gradual Maximum Information Ratio (GMIR)
9) Efficiency Balanced Information (EBI)
1. Maximum Fisher Information
One of the most widely used—and probably the oldest—item selection methods in computerized
adaptive testing (CAT) involves selecting an item with the maximized Fisher information (MFI)
at the interim proficiency estimate based on test items previously administered to the examinee.
Basically this involves finding item x maximizing
proficiency estimate
for an examinee with the interim
and m-1 as the number of items administered so far (Weiss, 1982). Taking
a typical case of a multiple-choice item pool, where item characteristics are defined by the threeparameter logistic model, or 3PLM (Birnbaum, 1968), the item selection method based on the
MFI criterion looks for item i that results in the largest value of
I [θ m −1 ] =
i
( Dai ) 2 (1 − ci )
[ci + e Dai (θ m−1 −bi ) ][1 + e− Dai (θ m−1 −bi ) ]2
,
(1)
where ai, bi, and ci are the discrimination, difficulty, and pseudo-guessing parameters in 3PLM,
respectively, and D is a scaling constant whose value is 1.702. The MFI criterion is popular
because it is an effective means of administering CAT that results in maximized test information
for each individual. In the early stage of testing, however, when five or fewer items have been
administered, for example, the interim proficiency estimates are rarely accurate. So as testing
begins, items selected according to the MFI criterion tend not to provide as much information as
User’s Manual for SimulCAT 5
they were designed to do at interim proficiency estimates. Another issue with the MFI method is
that it tends to select items with higher a-parameter values more frequently than it selects items
with lower a-parameter values. This uneven item usage with the MFI method may create serious
problems in item pool maintenance.
2. a-Stratification With/Without b-Blocking
To prevent wasting items with higher a-parameter values at the outset of CAT administration,
Chang and Ying (1999) proposed stratifying items in the item pool by a-parameter values. In
their method, known as a-stratification, items with b-parameter values closest to the interim
are selected from the item stratum with the lowest a-parameter values at CAT’s outset. Using
this method, items with higher a-parameter values are selected from the item strata as CAT
administration proceeds.
A potential problem with this method is an observed correlational relationship between a- and bparameter values, such that when items are stratified according to a-parameter values the item
strata may not be equivalent to each other in terms of b-parameters. Chang, Qian, and Ying
(2001) addressed this problem with their modification known as a-stratification with b-blocking.
3. Best Matching b-Value
The best matching b-value criterion, essentially is a special application of the a-stratification
method that always uses only one item stratum. With this method, an item with a b-value closest
to the interim theta estimate is selected regardless a- and c-parameter values.
4. Randomization
With this item selection method, an item is picked at random; thus the test is not adaptive.
5. Interval Information Criterion
Veerkamp and Berger (1997) designed two alternatives to MFI. In the first, called the interval
information criterion (IIC), the information function is averaged across the confidence interval
of an interim proficiency estimate. The mathematic expression of IIC for item i is
User’s Manual for SimulCAT 6
θ R
∫θ θ
=L
where
L
and
R
I i [θ ]dθ
(2)
,
are a confidence interval of θ. The actual mean value for IIC is Equation 2
divided by the length of the confidence interval; however taking an average of it is unnecessary
for the purpose of item selection.
6. Likelihood Weight Information Criterion
In the second alternative approach proposed by Veerkamp and Berger (1997), the likelihood
weighted information criterion (LWI), the information function is summed throughout the theta
scale, weighted by the likelihood function after item administrations performed thus far. With the
LWI criterion, the item to be selected is item i that results in the maximized value of
∞
∫θ
=−∞
L(θ ; xm−1 ) I i [θ ]dθ
,
(3)
where L(θ;xm-1) is the likelihood function of the response vector xm-1 after (m-1)th item
administration.
7. Kullbak-Leibler Information (Global Information)
Chang and Ying (1996) came up with the global information approach that uses the moving
average of Kullback-Leibler information (KLI) to select items (Cover & Thomas, 1991;
Kullback, 1959). The KLI for any θ for the ith item with response Xi is defined by
⎡ P (θ ) ⎤
⎡1 − Pi (θ 0 ) ⎤
K i (θ || θ 0 ) = Pi (θ 0 ) log ⎢ i 0 ⎥ + [1 − Pi (θ0 )]log ⎢
⎥,
⎣ Pi (θ ) ⎦
⎣ 1 − Pi (θ ) ⎦
(4)
where Pi(θ0) is the probability that a random examinee at the proficiency level θ0 answers the
item correctly. The moving average of KLI is then calculated and used as the item selection
criterion, as follows,
K i (θ 0 ) = ∫
θ 0 +δ
θ 0 −δ
K i (θ || θ 0 ) dθ ,
(5)
where δ specifies the range of the moving average. Determining δ could yield ambiguous results,
but Chang and Ying (1996) proposed c / m as a reasonable choice for δ with constant c selected
according to a specified coverage probability and with m being the number of items administered
thus far. Chang and Ying (1996) found that replacing the MFI criterion with the KLI criterion
User’s Manual for SimulCAT 7
often reduced the biases and mean-squared errors of proficiency estimation when the test length
was short or the CAT administration was in its early stage (m < 30).
8. Gradual Maximum Information Ratio (GMIR)
To promote use of items with low a-parameter values, Han (2009) proposed selecting items at
the beginning of CAT administration based on expected item efficiency instead of the MFI
criterion. Expected item efficiency is defined as the level of realization of an item’s potential
information at interim . Thus, if item i results in its maximum potential information at
expected item efficiency at interim
, the
is computed by
I i [θ m −1 ]
I i [θ i* ] ,
(6)
where θ i* is equal to bi when either a 1PL or 2PL model is used. If a 3PL model is used and ci ≠ 0,
θ i* can be computed using Birnbaum’s solution (1968):
θi* = bi +
1 + 1 + 8ci
1
log(
).
Dai
2
(7)
Han (2009) suggested taking item effectiveness (i.e., expected item information) into account
over the item efficiency as CAT administration proceeds and reaches its conclusion. This
approach looks for an item that maximizes the criterion,
I i [θ m −1 ]
m
m
(1 − ) + I i [θ m −1 ]
*
I i [θi ]
M
M ,
(8)
where M is the test length, and m is 1 plus the number of items administered thus far. This
method is referred to as the gradual maximum information ratio (GMIR) approach. The first part
of Equation 8 is the item efficiency term; the second part is the item effectiveness term (the
Fisher information from Equation 1). Each part of Equation 8 is inversely weighted by the
progress of the CAT administration. Based on his simulation results, Han (2009) found that the
GMIR approach could generally improve the item pool utilization compared to the MFI criterion.
9. Efficiency Balanced Information (EBI)
Han (2010) proposed the efficiency balanced information (EBI) criterion for item selection.
User’s Manual for SimulCAT 8
Unlike the GMIR approach (Han, 2009), the item efficiency (Equation 6) and information are not
evaluated at a certain point of θ but assessed across the θ interval. The width of the θ interval for
evaluation of item efficiency and information is determined by standard errors of estimation
(SEE; ε) and set to 2SEE from
after j-th item administration (
EBI i [θ j ] = (1 +
2ε ).
θ j + 2ε j
1
)
I i [θ ]dθ ,
I i [θ i* ] ∫θ j − 2ε j
With this method, items with lower a-values are more likely to be selected at the beginning of
CAT whereas items with higher a-values occur more frequently in CAT’s later stages.
(9)
User’s Manual for SimulCAT 9
III. Item Exposure Controls Used Within SimulCAT
The SimulCAT software tool for CAT simulation offers five item exposure control methods: (1)
randomesque, (2) Sympson-Hetter, (3) unconditional multinomial, (4) conditional multinomial,
and (5) the fade-away method.
1. Randomesque
Kingsbury and Zara (1989) proposed the randomesque method to keep the best item from being
solely (or excessively) used in CAT administration. In this method, a certain number of the best
items are selected, one of which is administered randomly. The randomesque method may not be
highly effective in limiting the overall item exposure rate to a target rate but it can prevent the
same item from being used repeatedly for test takers with similar proficiency.
2. Sympson-Hetter Method
In the probabilistic approach developed by Sympson and Hetter (1985), the probability P(A) that
an item will be administered is differentiated from the probability P(S) that the item will be
selected by the item selection algorithm. In other words, the Sympson-Hetter method introduces
the conditional probability P(A|S) that the selected item actually will be administered. In order to
keep the P(A) at a desirable target level, the P(A|S) that results in the target P(A) is derived from
iterative simulations. Once the P(A|S) is computed for each item in the item pool, it is treated as
the exposure parameter in the actual item selection process. During CAT administration, all
eligible items are ordered by a choice of item selection criterion. Starting from the best item, the
item exposure parameter is compared to a randomly generated value between 0 and 1 (following
a uniform distribution). If the random value is smaller than the exposure parameter, the item is
administered; otherwise, the process proceeds to the next best item. This process is repeated until
one item is finally administered. It is important to note that the computed exposure parameters
are pool-specific—in other words, the exposure parameters should be recomputed whenever
there is a change in the item pool.
3. Unconditional Multinomial Method
The unconditional multinomial (UM) method (Stocking & Lewis, 1995) is similar to the
User’s Manual for SimulCAT 10
Sympson-Hetter (SH) method in computing exposure parameters using iterative simulations. The
major difference between the UM method and the SH method is that the UM method forms a
multinomial distribution from each item’s P(A|S) first and then compares the distribution to a
random value to determine which item to actually administer.
4. Conditional Multinomial Method
The SH and UM methods are useful for controlling overall exposure for each item but they don’t
guarantee a desired exposure rate within each group of test takers of similar proficiency. In the
conditional multinomial (CM) method (Stocking & Lewis, 1998), each item has multiple
exposure parameters corresponding to each proficiency group. The exposure parameters are
computed separately for each proficiency group during the simulations. Once the exposure
parameters are computed, the exposure parameter for the corresponding proficiency group based
on the (interim) theta estimate is used to form a multinomial distribution. The rest of the
procedure is the same as the UM method.
5. Fade-Away Method
Today’s computer networking technology makes it possible for main computer servers and client
computers (i.e., test terminals) in test centers to communicate before, during, and/or after CAT
administration to reconfigure a variety of test information including item use. Complete item
usage information maintained in the main server can be updated regularly by the client
computers during or after each CAT administration via the online network. In addition, each
client computer can access updated item usage information from the server just before the start
of the next test administration. Such network technology enables the CAT system to use near
real-time item exposure information for the exposure control, precluding the need to predict the
item exposure by other means, for example, using the Sympson-Hetter method (Sympson &
Hetter, 1985), which involves iterative simulations.
In the new item exposure control method, the item selection criterion value for each eligible item
in the pool is inversely weighted by the ratio between the updated actual exposure rate and the
target exposure rate. For example, with the MFI criterion displayed in Equation 6, CAT looked
for an item that maximized
User’s Manual for SimulCAT 11
U
I i [θ m −1 ] i ,
C
(6)
where C was the absolute item usage limit (of the first exposure control component), which was
3,000 in this study. Ui was the item usage for the life of item i. With this new method, rarely
used items are expected to be promoted more frequently, and excessively used items are likely to
“fade away” from the item selection. This method will be referred to hereafter as the fade-away
(FAM) method.
User’s Manual for SimulCAT 12
IV. Content Balancing Methods Used Within SimulCAT
SimultCAT employs two content-balancing methods—the script method and weight method.
1. Script Method
In the script method, test content is controlled by a script that specifies the content area based on
test administration progress. The program randomly selects one script among many available
scripts to prevent test takers from predicting the sequence of content areas (Note: The current
version of SimulCAT supports only one script). When the script is shorter than the actual test
length, it will restart from the top after the last content area in the script is administered.
2. By Weight
Kingsbury and Zara (1989) proposed the constrained CAT (CCAT) method to balance content
areas. In CCAT, the content area from which an item will be selected for administration is
determined by the difference between the target weight and actual percentage of each content
area thus far administered; thus the system selects the content area with a percentage farthest
from the target weight.
User’s Manual for SimulCAT 13
V. Using SimulCAT With Graphical User Interface (GUI)
This section of the manual provides step-by-step instructions for setting up and simulating
various CAT administration options, with illustrations of the actual graphical interface used in
the SimulCAT program. Step 1 explains how to generate examinee and item pool data. Step 2
details how to specify an item selection algorithm by setting item selection criteria, item
exposure control, test length, and content balancing. Step 3 includes instructions for specifying
CAT administration rules regarding score estimation, test administration and pre-test
administration, and allows the user to specify extra features and output formats before running a
CAT simulation. It also contains information on running example scenarios.
Step 1. Generating Examinee and Item Pool Data
A. Examinee Characteristics (Green Box)
User’s Manual for SimulCAT 14
1. Specify the number of examinees.
2. Select type of score distribution .
3. Specify mean and standard deviation for a normal score distribution or, specify minimum
and maximum value for a uniform score distribution or, specify a and b parameters for a
beta score distribution.
4. Click on the green ‘Generate True Scores’ button.
5. Generated examinee theta scores should display in the box. The data set can be saved at
‘File > Save > Examinee.’
6. Distribution of examinee thetas can be shown by clicking on the ‘Histogram’ button.
B. Item Characteristics (Blue Box)
1. Specify the number of items.
2. Select distribution of item parameters and specify properties of the distributions.
3. Specify the content ID (area code) for the items being generated.
4. Click on the red ‘Generate’ button.
5. Generated item parameter data should then display in the box. The data set can be saved
at ‘File > Save > Item.’
6. Item characteristic curves (ICCs), the item pool characteristic curve, item information
function curves (IIF), and the pool information function curve (PIF) can be displayed by
clicking on the ‘Plot Item(s)’ button.
7. Check the box labeled, ‘Add to the previous item set’, and repeat steps 1 through 4 if you
need to add another set of items (or items with different content IDs) to a previous set of
items. This option is particularly useful when simulating an item pool with multiple
content areas.
[Note: The current version of SimulCAT only supports the three parameter logistic model
(3PLM) .]
User’s Manual for SimulCAT 15
Step 2. Specifying Item Selection Algorithm
A. Item Selection Criterion (Green Box)
1. Select one of the nine item selection criterion (methods) listed in the box. (For detailed
descriptions of each item selection criterion, see Chapter II.
B. Item Exposure Control (Blue Box)
1. Select the level of item exposure control for your CAT simulation. You can choose to
have no exposure control, or you can select one of several options for exposure control.
(For detailed information about each item exposure control method, see Chapter III.)
2. (Optional) Check “Cumulative Item Usage Criterion for Retirement,” if you want items
to retire when they reach a specified cumulative usage level. Once the items retire, they
no longer will be considered in item selection.
User’s Manual for SimulCAT 16
3. If you select the Fade-Away method and/or choose the item retirement option, you must
specify the “Item Usage Update” frequency. The item usage update frequency is the
frequency of the reconsolidation between the test server and test terminals. (For more
information, see Chapter III, Section 5.)
C. Test Length (Brown Box)
1. If “Fixed Length” is selected, specify the number of items for each individual.
2. If “Variable Length” is selected, specify the CAT termination rules.
a) The termination rules are combined by an “or” operation, which means the CAT
administration is terminated when any of the CAT termination rules are satisfied.
b) Unlike the other three rules, the “minimum” rule will not terminate CAT until the test
length reaches the specified minimum length even if one or more other termination rules
were satisfied.
c) If the a-Stratification or GMIR methods were chosen for item selection, the expected test
length must be specified. Both of these item selection methods compute test progress
based on expected test length.
D. Content Balancing (Pink Box)
1. Select your preferred content balancing format, either “By Script” or “By Weight,” or
select None. The input file formats for Script and Weight differ. See Chapter VI, Section
2, for detailed information about each content balancing method.
[IMPORTANT NOTE: The content area (content ID) is determined before the item selection
criterion and exposure control are selected.]
User’s Manual for SimulCAT 17
Step 3. Specifying CAT Administration Rules
A. Score Estimation (Green Box)
1. Select MLE, MAP, or EAP for estimating interim and final scores.
a. Specify posterior mean and SD values if you selected MAP or EAP. (The default
values for posterior mean and SD are 0 and 1, respectively).
2. Specify the initial score value. The initial score value can be fixed, randomly drawn, or
loaded with a preexisting data (*.wge file).
a. The default setting randomly draws a value from a uniform distribution (-0.5, 0.5).
3. (Optional) You can opt to specify the range of score estimates. Estimates that are out of
the specified range will be truncated.
User’s Manual for SimulCAT 18
4. (Optional) In the early stage of CAT, score estimates often are unstable (especially with
the MLE method). You can choose to limit the level of fluctuation in estimates during the
first several item administrations.
5. (Optional) You can choose to have final score estimates computed using MLE even if
you selected MAP or EAP as the main estimation method.
B. Test Administration (Orange Box)
1. Specify the number of examinees that for each time slot in the simulated CAT
administration. If you want to administer CAT with all examinees simultaneously, put “0”
(default) in “Number of Examinees for Each Test Time Slot.” Note: The program
assumes that all examinees for each test time slot make CAT progress at the same pace.
2. Specify “Number of Test Time Slots per Day.” A default value is “1.”
(These inputs are closely related to “Item Usage Update” in “Exposure Control.”)
C. Pretest Item Administration (Blue Box)
1. Specify the number of pretest items to be administered with each examinee. The pretest
item pool data file (in *.wgi or *.wgix format) should be loaded using the “Open Pretest
Item File” button. The pretest items are randomly selected for each examinee, and
examinees’ responses will not be used for scoring. The pretest item administration results
will be stored in a separate file (*.scp).
D. Extras (Brown Box)
1. Generate Replication Data Sets: SimulCAT will replicate as many CAT simulations as
specified here.
2. Item Pool with DIF/Drift: To simulate CAT with DIF/item parameter drift (IPD), check
this box and provide an item pool data file containing the DIF/IPD affected item
parameter values. The DIF/IPD item pool data file (*.wgi or *.wgix) must have item
parameters for all items (even if items are not all of DIF/IPD). SimulCAT uses the
DIF/IPD item parameters only to generate responses. During the item selection process,
SimulCAT uses the original item pool data.
User’s Manual for SimulCAT 19
3. Previous Item Usage Data: Check this box only if you selected the item retirement option
in Exposure Control and there is preexisting item usage data.
4. Fixed Seed Value: Fix the seed value for simulation. This is useful if you want to
replicate the exact same study.
E. Outputs (Pink Box)
1. Select how you want to store the simulation results in the output file (*.sca). The item use
information will be stored in a separate file (*.scu). A full response matrix (optional) will
be stored in a separate file (*.dat).
F. Simulation Run (Black Box)
1. Specify the filename of the main output file (*.sca).
2. After reviewing all your selections in Steps 1, 2, and 3, click the “Run Simulation” button
to run the CAT simulation.
3. Messages from SimulCAT and the progress of CAT simulation will be displayed in the
“Log/Message” box.
G. Examples
To run examples, select “File>Open>Syntax” and choose an example syntax file. Once a syntax
file is successfully loaded, review all settings throughout Steps 1, 2 and 3. Click “Run Simulation”
in Step 3. For more information about file formats used in SimulCAT see Chapter VI. For more
information about SimulCAT syntax commands, see Chapter VII.
Example Scenario 1 (Example syntax file: Example_syntax_I1E3V.scs)
1,000 examinees from a normal distribution N(0,1) (from a data file, “Example_simulee1000.wge”)
Item pool with 500 items (from a data file, “Example_ItemPool500.wgix”)
Maximum Fisher Information Criterion for item selection
Randomesque method for item exposure control
Initial theta estimate is a random value between -0.5 and 0.5
Interim theta is estimated using the EAP method.
Final theta is estimated using the MLE method.
User’s Manual for SimulCAT 20
VI. SimulCAT File Formats
1. File Extensions
SimulCAT uses and produces several kinds of input and output files. Unique extensions are
assigned to files according to their purpose. Several file formats are the same as ones that are
used with WinGen (Han, 2007a, 2007b). Table 6.1 summarizes the types of files associated
with SimulCAT.
Table 6.1 Extensions of SimulCAT Files
Extension
Description
*.cue
SimulCAT cue file for executing sets of syntax files
*.log
SimulCAT log (for each ‘Run Simulation’)
*.wge
WinGen/SimulCAT data file for examinees
*.wgi
WinGen data file for Item Parameters (without content variables)
*.wgix
SimulCAT data file for Item Parameters (with content variables)
*.dat
*.sca
*.scc
SimulCAT output for full response data matrix
SimulCAT output for CAT administration
SimulCAT input for content balancing information (two different
formats exist)
SimulCAT data file for item exposure parameters
*.sce
*.scs
*.scp
*.scu
SimulCAT syntax file
SimulCAT output for response data for pretesting items
SimulCAT output for item usage information
Can be used as ‘previous item exposure’ data.
Type
Input only
Output only
Input and
output
Input only
Input and
output
Output only
Output only
Input only
Input and
output
Input only
Output only
Input and
output
2. SimulCAT File Formats
All input and output files of SimulCAT are ASC text file format and can be opened and edited
with Notepad, TextPad, MS Excel, SPSS, SAS,etc.
User’s Manual for SimulCAT 21
A. Sample File Format : WinGen/SimulCAT Examinee Data File (*.wge) – ‘tab-delimited’
Format: [Examinee #][Theta]
B. Sample File Format: WinGen/SimulCAT Item Parameter Data File (*.wgi) – ‘tab-delimited’
Format: [Item#][Model][# of categories][a-parameters][b-parameters][c-parameters]
User’s Manual for SimulCAT 22
Models available [NOTE: SimulCAT currently does not support any polytomous response
models, e.g., GRM, PCM, GPCM, NRM, and RSM.]:
•
1PLM: One Parameter Logistic Model
•
2PLM: Two Parameter Logistic Model
•
3PLM: Three Parameter Logistic Model
•
GRM: Graded Response Model
•
PCM: Partial Credit Model
•
GPCM: General Partial Credit Model
•
NRM: Nominal Response Model
RSM: Rating Scale Model
C. SimulCAT Extended Item Parameter Data File (*.wgix) – ‘tab-delimited’
Format: [Item#][Content Code][Model][# of categories][a-parameters][b-parameters][cparameters]
The only difference between the *.wgix format and *.wgi is additional information about content
(content code, which always has to be integer) after the item number. This is a mandatory format
if content balancing is performed in the simulation.
Example File> Example_ItemPool500.wgix
D. SimulCAT Administration Result File (*.sca) – ‘tab-delimited’ (partially ‘comma-delimited’
for a list of interim values)
Format:[Replication # (only if there is more than one replication)]
[Day #]
[Slot #]
[Examinee #]
[True theta value]
[# of items administered]
[Final theta estimate]
[SEE for the final theta estimate]
[Response string (if the output option was selected)]
[Administered item IDs (if the output option was selected)]
User’s Manual for SimulCAT 23
[Initial & interim theta estimates (if the output option was selected)]
[Interim SEEs (if the output option was selected)]
[Interim test information (if the output option was selected)]
[True interim SEEs (if the output option was selected)]
[True interim test information (if the output option was selected)]
Example File> Example_output_I2E4F.SCA (with an option for saving response strings and
administered item IDs)
E. SimulCAT Item Usage (Exposure) Data File (*.scu) – ‘tab-delimited’
Format: [Replication # (only if there are more than one replication)][Item #][# of item
administration] [Retirement day if the item was retired during the test window]
Example File> Example_output_I1E3V.SCU
F. SimulCAT Item Exposure Parameter File (*.sce) – ‘tab-delimited’
Format: [Item #][Exposure parameter]
Example File> Example_SCE_for_SHM.SCE
[NOTE: *.sce file for the conditional matrimonial method (CMM) has additional information in
the first line; [# of intervals], [lower bound], [upper bound] ]
Example File> Example_SCE_for_MCC.SCE
G. SimulCAT pretesting item administration data file (*.scp) – ‘tab-delimited’
Format: [Examinee ID (8 characters)][blank (2 spaces)]
[True theta value (6 characters)][blank (2 spaces)]
[Final score estimate (6 characters)][blank (2 spaces)]
[Response data]
H. SimulCAT Full Response Matrix File (*.dat) – fixed format
Format: [Examinee ID(8 characters)][blank (2 spaces)][Response data]
Example File> Example_output_I2E4F.DAT
User’s Manual for SimulCAT 24
VII. Advanced Uses of SimulCAT
Using a Syntax File
A syntax file can be used to run SimulCAT instead of the point-and-click method of the graphical
user interface. Syntax files for WinGen can be composited using any kind of text editing
software such as ‘Notepad’ or ‘TextPad’.
The structure of a syntax file is straightforward—there is one command/option per line. Each
line starts with an abbreviation for the corresponding section in the interface, followed by “>”
and a choice of options. If an option has multiple inputs, they should be delimited by “,”
(comma). See the example below for an illustration.
It should be noted that when SimulCAT runs with a syntax file, it can only read existing data for
examinee and item characteristics. To generate random examinee and/or item data, SimulCAT
should be used with the graphical user interface, not with a syntax file. Text/syntax after “!” is
User’s Manual for SimulCAT 25
recognized as a ‘comment’ and ignored by SimulCAT. Table 7.1 displays the complete list of
abbreviations and options for a syntax file.
Table 7.1 Abbreviations /Options for SimulCAT Syntax Files
Abbreviation
EC
(Examinee Characteristics)
IC
(Item Characteristics)
Option
[‘file,’ a full filename with a complete directory name]
e.g.
EC> file, c:\simulcatStudy\examinee.wge
[‘file,’ a full filename with a complete directory name]
e.g.
IC> file, c:\simulcatStudy\item.wgix
[‘normal’] – scale to normal metric (D=1.702 instead of 1.0)
e.g.
IC> normal
ISC
(Item Selection Criteria)
[‘MFI’] – the maximum Fisher information. e.g.
ISC> MFI !MFI method
[‘STRA,’ # of strata, ‘BB’] – the a-stratification method. The number of strata
should be specified after a comma.
e.g.
ISC> STRA, 4 !a-stratification with 4 strata
IEC
(Item Exposure Control)
To select ‘b-blocking’, [‘BB’] should be followed after the number of strata.
e.g.
ISC> STRA, 4, BB !a-stratification with b-blocking (with 4 strata)
[‘MAT’] – the matching b-value method.
[‘RAN’] – the randomization method.
[‘IIC’] – the interval information criterion (IIC).
[‘LWI’] – the likelihood weighted information (LWI).
[‘KLI,’ constant c value, # of items for randomesque] – the Kullbak-Leibler (global)
information (KLI). For this option, the value of the constant ‘c’ should be specified.
e.g.
ISC> KLI, 3, 2 !KLI with constant c=3 with the randomesque with 2 items.
[‘GMIR’] – the gradual maximum information ratio method.
[‘EBI’] – the efficiency balanced information method.
[‘NON’] – no exposure control.
[‘FAM,’ exposure target] – the fade-way method. For this option, the exposure rate
target should be specified.
e.g.
IEC> FAM, 0.2
[‘RAN,’ # of items for randomesque] - the randomesque method. The number of
items for the randomesque procedure also should be specified after a comma.
e.g.
IEC> RAN, 2 !the randomesque with 2 items.
User’s Manual for SimulCAT 26
Table 7.1 Abbreviations /Options for SimulCAT Syntax Files
Abbreviation
Option
[‘SHM, FILE,’ the full filename of a *.sce file] – the Sympson and Hetter method
with pre-computed exposure parameter data. e.g.
IEC> SHM, FILE, c:\simulcatStudy\expo.sce
[‘SHM,’ # of iterations, exposure target] – the Sympson and Hetter method after
computing the exposure parameters for the specified exposure rate target.
e.g.
IEC> SHM, 30, 0.2
[‘UCM,’ # of iterations, exposure target] – the unconditional multinomial method
after computing the exposure parameters for the specified exposure rate target.
e.g.
IEC> UCM, 30, 0.2
[‘CCM,’ # of iterations, exposure target, # of intervals for theta, lower bound of theta
interval, upper bound of theta interval] – the conditional multinomial method after
computing the exposure parameters for the specified exposure rate target .
e.g.
IEC> CCM, 30, 0.2, 6, -3, 3
[‘CCM, FILE,’ the full filename of a *.sce file] – the conditional multinomial
method with pre-computed exposure parameter data. Note that *.sce files contain the
interval information in the first line.
e.g.
IEC> CCM, FILE, c:\simulcatStudy\expo.sce
[‘RET,’ target item usage] – letting items permanently retire once their usage
reaches to the target
e.g.
IEC> RET, 3000
[‘UPDATE,’ [‘REAL’ or ‘SLOT’ or ‘DAY’] – frequency of item usage update.
e.g.,
IEC> UPDATE, SLOT
TL
(Test Length)
[‘FIX,’ X] – fixed length test. X items will be administered.
e.g.
TL> FIX, 30
[‘VAR’] – variable length test. Additional information about termination rules
should be specified in separate lines. At least one termination rule has be specified
(among SEE, EST, and MAX).
[‘SEE,’ X] – terminating CAT when SEE of examinee’s score estimate reaches X.
[‘EST,’ X, Y] – terminating CAT when examinee’s score estimate does not change
by X for the last Y item administrations.
[‘MAX,’ X] – terminating CAT when the number of administered items reaches X.
This rule overrules SEE and EST rules.
User’s Manual for SimulCAT 27
Table 7.1 Abbreviations /Options for SimulCAT Syntax Files
Abbreviation
Option
[‘MIN,’ X] – keeping from terminating before the number of administered items
reaches X. This rule overrules SEE and EST rules.
e.g.,
TL> VAR !CAT is variable length.
TL> SEE, 0.3 !CAT is terminated when SEE<=0.3
TL> EST, 0.1 ,5 !CAT is terminated when theta estimate does not change by
0.1 for the last five item administrations.
TL> MAX, 40 !CAT is terminated when 40 items are administered
regardless of SEE and EST values.
TL> MIN, 10 !CAT is not terminated before at least 10 items are
administered.
CB
(Content Balancing)
SE
(Score Estimation)
[‘EXP,’ #] – expected test length. This is required information when the astratification or GMIR method was selected for item selection and when the test
length is variable.
e.g.,
TL> EXP, 30 !User expects a typical length of CAT would be 30 items.
[‘NON’] – no content balancing
[‘SCR,’ a full filename with a complete directory name] – content balancing by a
script.
e.g.,
CB> SCR, c:\simulcatStudy\script.scc
[‘WGT,’ a full filename with a complete directory name] – content balancing by a
weight (or percentage).
e.g.,
CB> WGT, c:\simulcatStudy\script.scc
[‘MLE’] – the maximum likelihood Estimation
[‘MAP,’ X, Y] – the Bayesian maximum a posteriori estimation with a posterior
distribution with mean of X and SD of Y.
e.g.,
SE> MAP, 0, 1 !MAP estimation with a posteriori of N(0,1)
[‘EAP,’ X, Y] – the Bayes expected a posteriori estimation with a posterior
distribution with mean of X and SD of Y.
e.g.,
SE> EAP, 0, 1 !EAP estimation with a posteriori of N(0,1)
[‘FIX,’ X] – the initial score is fixed to X.
[‘RAN,’ X, Y] – the initial score is a random value between X and Y.
e.g.,
SE> RAN, -0.5, 0.5 !Initial theta value is a random value between -0.5 and
0.5.
[‘FILE,’ X, a full filename with a complete directory name] – the initial score is
loaded from an existing data file (*.wge).
e.g.,
SE> FILE, c:\simulcatStudy\oldScore.wge
[‘TRUNC,’ X, Y] – the score estimates are truncated to be between X and Y.
e.g.,
SE> TRUNC, -3, 3 !Theta estimates are truncated to be b/w -3 and 3.
User’s Manual for SimulCAT 28
Table 7.1 Abbreviations /Options for SimulCAT Syntax Files
Abbreviation
Option
[‘JUMP,’ X, Y] – the change in score estimate cannot exceed X from the previous
estimate until Yth item administration.
e.g.,
SE> JUMP, 1, 5
TA
(Test Administration)
EXT
(Extras)
[‘FINAL’] – the final score is estimated using the MLE regardless a choice of
proficiency estimation method.
e.g.,
SE> FINAL
[X, Y] – X is the number of examinees taking the exam at the same time (i.e., the
maximum seating capacity of testing centers). Y is the number of testing slots per
day. If all examinees are to be administered simultaneously, put “0, 0”, which is the
default.
e.g.,
TA> 500, 2
!500 examinees are administered in each testing slot. Two testing slots are
administered per day. (i.e., 1000 examinees per day)
[‘REP,’ X] – Replicating the simulation X times.
[‘DIF,’ a full filename with a complete directory name] – Introducing DIF/IPD from
the item parameter data (*.wgi or *.wgix).
[‘EXP,’ a full filename with a complete directory name] – Setting the initial item
usage values to the previous item usage value (*.scu).
[‘SEED,’ X] – Using X as a SEED value for simulation.
e.g.,
EXT> REP, 10 !Replicates 10 times
EXT> DIF, c:\simulcatStudy\DIF_Param.wgi
!Examinees’ responses are simulated based on the DIF item parameters.
EXT> EXP, c:\simulcatStudy\prevUsage.scu
!item usage information incorporates the previous information.
EXT> SEED, 61346125 !SEED value is 61346125
PIA
(Pretest Item
Administration)
OUT
(Outputs)
[‘IP,’ item pocket size] – simulating the worst case scenario for item pocket option.
[‘NON’] – no precalibrated item to be administered.
[X, a full filename with a complete directory name] – administering X pretesting
items to each examinee from a pretesting item pool (*.wgi or *.wgix).
e.g.,
PIA> 5, c:\simulcatStudy\preTestingItems.wgi
!Each examinee takes 5 precalibrated items that are randomly selected from
‘preCalItems.wgi’.
[’SAVE, RES’] – Saving the response strings and item IDs in *.sca.
[’SAVE, THE’] – Saving all interim theta estimates in *.sca.
[’SAVE, SEE’] – Saving all interim SEE and test information values in *.sca.
[’SAVE, TRU’] –Saving all interim SEE and test information values at the true theta
in *.sca.
[’SAVE, USE’] – Saving item usage information in *.scu.
[’SAVE, USE’] – Saving item usage information in *.scu.
User’s Manual for SimulCAT 29
Table 7.1 Abbreviations /Options for SimulCAT Syntax Files
Abbreviation
Option
[’SAVE, FULL’] – Saving a full response matrix in *.dat.
e.g.,
OUT> SAVE, RES
OUT> SAVE, THE
OUT> SAVE, SEE
OUT> SAVE, USE
Cue File
A cue file is a batch file with which SimulCAT runs multiple syntax files. Basically, it is a list of
the full names of the syntax files. A cue file can be executed at “File>Run a Cue File” on the
program menu bar.
Example of a Cue File
User’s Manual for SimulCAT 30
References
Birnbaum, A. (1968). Some latent trait models and their use in inferring an examinee’s ability. In
F. M. Lord & M. R. Novick (Eds.), Statistical theories of mental test scores (Chaps. 1720). Reading, MA: Addison-Wesley.
Chang, H.-H., Qian, J., & Ying, Z. (2001). Alpha-stratified multistage computerized adaptive
testing with beta blocking. Applied Psychological Measurement, 25, 333–341.
Chang, H.-H., & Ying, Z. (1996). A global information approach to computerized adaptive
testing. Applied Psychological Measurement, 20, 213–229.
Chang, H.-H., & Ying, Z. (1999). Alpha-stratified multistage computerized adaptive testing.
Applied Psychological Measurement, 23, 211–222.
Cover, T. M., & Thomas, J. A. (1991). Elements of information theory. New York: Wiley.
Kullback, S. (1959). Information theory and statistics. New York: Wiley.
Han, K. T. (2007a). WinGen: Windows software that generates IRT parameters and item
responses. Applied Psychological Measurement, 31(5), 457-459.
Han, K. T., & Hambleton, R. K. (2007b). User's Manual: WinGen (Center for Educational
Assessment Report No. 642). Amherst, MA: University of Massachusetts, School of
Education.
Han, K. T. (2009). A gradual maximum information ratio approach to item selection in
computerized adaptive testing. Research Reports 09–07, McLean, VA: Graduate
Management Admission Council.
Han, K. T. (2010). SimulCAT: Simulation software for computerized adaptive testing [computer
program]. Retrieved March 20, 2010, from http://www.hantest.net/
Kingsbury, G. G., & Zara, A. R. (1989). Procedures for selecting items for computerized
adaptive tests. Applied Measurement in Education, 2(4), 359–375.
Stocking, M. L., & Lewis, C. (1995). A new method of controlling item exposure in computerized
adaptive testing. Research Report 95–25. Princeton, NJ: Educational Testing Service.
Stocking, M. L., & Lewis, C. (1998). Controlling item exposure conditional on ability in
computerized adaptive testing. Journal of Educational and Behavioral Statistics, 23(1),
57–75.
Sympson, J. B. & Hetter, R. D. (1985). Controlling item-exposure rates in computerized
adaptive testing. In Proceedings of the 27th annual meeting of the Military Testing
Association, (pp. 973–977), San Diego, CA: Navy Personnel Research and Development
Centre.
User’s Manual for SimulCAT 31
Veerkamp, W. J. J., & Berger, M. P. F. (1997). Some new item selection criteria for adaptive
testing, Journal of Educational and Behavioral Statistics, 22(2), 203–226.
Weiss, D. J. (1982). Improving measurement quality and efficiency with adaptive testing.
Applied Psychological Measurement, 6, 473–492.
Acknowledgements
The author is very grateful to Ronald K. Hambleton of the University of Massachusetts in
Amherst for important feedback. The author also wishes to thank Lawrence M. Rudner and
Fanmin Guo of the Graduate Management Admission Council® for valuable comments and
support.
Author’s Address
Correspondence concerning SimulCAT should be addressed to Kyung T. Han, Graduate
Management Admission Council, 11921 Freedom Dr., Suite 300, Reston, VA 20190;
email: [email protected]
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