WinGen WinGen2 Simulation Software User's Manual

2007
User’s Manual: WinGen2 User’s Manual: WinGen 1
Header: User’s Manual: WinGen
User’s Manual for WinGen:
Windows Software that Generates IRT Model Parameters and Item Responses1
Kyung T. Han and Ronald K. Hambleton
University of Massachusetts Amherst
1
Center for Educational Assessment Research Report No. 642. Amherst, MA: University of Massachusetts, Center
for Educational Assessment.
User’s Manual: WinGen 2
Contents
I. Introduction
II. Item Response Models Available in WinGen
Unidimensional Dichotomous Models
4
10
10
Normal Ogive Model
One-Parameter Logistic Model (Rasch Model)
Two-Parameter Logistic Model
Three-Parameter Logistic Model
Nonparametric Model
Unidimensional Polytomous Models
Partial Credit Model
Generalized Partial Credit Model
Rating Scale Model
Graded Response Model
Nominal Response Model (Nominal Categories Models)
Multidimensional Dichotomous Model
Compensatory Three-Parameter Logistic Model
III. Quick Start
Generating Examinee Parameters
Generating Item Parameters
Generating Response Data
Options
IV. WinGen Files
File Extensions
22
User’s Manual: WinGen 3
File Naming Rules
File Formats
V. Advanced Uses of WinGen
Generating Response Data with DIF / IPD
Generating Multidimensional Item Response Data
Using Syntax Files and Cue Files
VI. References
43
User’s Manual: WinGen 4
I. Introduction
Item response theory (IRT) is a popular and valuable framework for modeling
educational and psychological test data, due to attractive properties such as the invariance of
item and examinee parameter values (when IRT models can be found that fit the test data) and
item parameters and examinee parameters being reported on a common scale. However, IRT
models often rely on or are based on two strict assumptions, unidimensionality and the
mathematical form of the item characteristic functions, and violations of these assumptions can
produce serious negative consequences to the measurement process. One way of evaluating the
impact of violating these two critical assumptions, as well as studying factors such as the impact
of choice of models, examinee sample sizes, the shape of ability distributions, and test length,
and many other factors, is via Monte Carlo simulation studies.
The essential part of Monte Carlo studies is simulating examinee item response data
given true model parameter values. A number of computer programs for simulating IRT data
have been developed since the early 1970s. However, most of them were developed in the DOS
environment (e.g., DATAGEN, Hambleton & Rovinelli, 1973, GENIRV, Baker, 1989, and
RESGEN, Muraki, 1992). As a result, these programs are limited today because of inherent
problems in DOS: (1) slow performance speed (16-bit), (2) limited usable system resources, (3)
incompatibility with recent 32-bit Windows-based OSs, and (4) not a user-friendly interface.
Some recent computer simulation programs, such as WINIRT (Fang & Johanson, 2005) and
PARDSIM (Yoes, 1997), were developed for Windows-based OSs, but they provide only a few
options for generating data from IRT models. Therefore, the primary goal of this project was to
develop computer software that could simulate IRT data using many IRT models and with many
User’s Manual: WinGen 5
important options to facilitate the design and implementation of computer simulation studies in
the field of psychometric methods.
A computer program, called WinGen (Han, 2006) was developed to generate
dichotomous and polytomous item response data for several IRT models and for many
conditions that arise in practice. WinGen has the following useful features:
1. WinGen supports various IRT models.
There are several kinds of unidimensional and multidimensional IRT models that are
widely used today: (1) dichotomous IRT models with one, two, and three parameters, (2) nonparametric models, (3) polytomous IRT models such as the partial credit model, generalized
partial credit model, graded response model, rating scale model, and nominal response model,
and, (4) multidimensional compensatory models. WinGen supports these IRT models and allows
users to have a mixture of more than one IRT model in a set of items (for example, data for the
first 10 items might be generated from the two-parameter logistic model, the next 30 items might
be generated from the three-parameter logistic model, and with the last 10 items, data might be
generated by the graded response model). Such a data set might be useful when simulating state
test data, for example.
2. WinGen generates IRT model parameter values from various distributions for realistic
data.
WinGen can generate sets of item parameters and sets of examinee ability parameters to
essentially create realistic item response data from various kinds of distributions. Most programs
that simulate IRT data only support normal and/or uniform distributions. Although uniform and
normal distributions may be theoretically ideal or easy to understand, these distributions are not
likely to be the only distributions seen in the real world or of interest to researchers. With
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WinGen a user can choose a normal, uniform, or beta distribution (which can be defined to allow
for the generation of skewed distributions, skewed from highly positive to highly negative) for
the examinee parameter in a model, and a normal, uniform, beta, or lognormal distribution for
item parameters so that the user can conduct a research study with more realistic IRT data sets,
or even unrealistic parameters, if that is the interest of the researcher.. WinGen provides a
graphic function of plotting a histogram of examinee ability parameters so that a user can make
sure the distribution of the generated parameters is what he/she wanted. This graphing feature is
especially helpful when the goal is to produce skewed distributions. Also, WinGen gives a user
substantial control over item and examinee parameters by allowing a user to enter user specified
parameter sets and/or to set SEED values for generating model parameters.
3. WinGen provides an intuitive and user-friendly interface.
By taking advantage of running on a Windows platform, WinGen provides a virtually point-andclick solution for simulating IRT data. There are three stages for simulating data: (1) generating
or reading in ability parameter values, (2) generating or reading in item parameter values, and (3)
simulating item response data. All three stages are shown on a one-stop interface screen, so a
user can reduce the number of possible mistakes by being able to check the simulated data at
each stage. Also, the intuitive interface of WinGen would be helpful for teaching IRT to those
who are not familiar with the theory. Once item parameters and/or ability parameters are
generated, WinGen immediately provides IRT plots such as item characteristic curves (ICC), test
characteristic curves (TCC), item information curves (IFC), and test information curves (TIC) so
that a user can make sure the generated parameters fit his/her research purposes. See Figure 1 for
an example of the interface.
User’s Manual: WinGen 7
Figure 1.1 WinGen provides an intuitive and user-friendly interface.
User’s Manual: WinGen 8
Figure 1.1 WinGen provides an intuitive and user-friendly interface (continued).
4. WinGen is based on the most recent computer environment.
WinGen was developed on Microsoft .NET frameworks 2.0, the most recent computer
software development environment. The program can run on either 32bit Windows series (ex.,
Windows XP) or 64bit Windows series (ex., Windows vista) and is optimized to use system
resources efficiently so that the program can handle a bigger data in a shorter time. This software
can also easily be converted to web-based software.
5. WinGen provides a powerful research tool.
User’s Manual: WinGen 9
Several powerful tools are provided for various research purposes in WinGen.
Replication data can be simulated up to 1,000,000 sets, and syntax files for other IRT programs,
such as PARSCALE (Muraki & Bock, 2003), BILOG-MG (Zimowski, Muraki, Mislevy, &
Bock, 2003), and MULTILOG (Thissen, 2003), are automatically generated (of course, a user
can specify the syntax of the software by reading in a sample syntax file). Batch files can also be
generated for handling multiple calibrations in a cue. WinGen provides a dialog input to
introduce differential item functioning (DIF) or item parameter drift in the simulated data. With
multiple file read-in option in WinGen, a user can have multiple groups of examinees and
multiple sets of items/tests. WinGen can also read-in output files (parameter estimates) from
other IRT programs and automatically analyze DIF by computing RMSD, MAD, and BIAS.
Table 1 summarizes the features of WinGen and several other simulation software available.
Educational Importance
Although many IRT model simulation software programs have been developed, most of
them were designed for intentionally narrow purposes since they were not publicly shared
programs. WinGen is more general and more user friendly than many of the IRT simulation
programs available today. WinGen is easy to use with an intuitive, user-friendly interface while
providing very strong research tools and performance at the same time. Thus, WinGen should be
useful for researchers who want to do simulation research, and students who are eager to learn
more about IRT.
User’s Manual: WinGen 10
Table 1.1. Comparison of IRT simulation programs.
Authors
Examinees
Items
OS
DATAGEN
Hambleton &
Rovinelli(1973)
4,000
400
DOS
IRT Models
1.Dichotomous
GENIRV
RESGEN
Baker(1989)
Muraki(1992)
4,000
100
1,000 (default)
100 (default)
DOS
1.Dichotomous
2.Polytomous
DOS
1.Dichotomous
2.Polytomous
3.Multidimensional
WINIRT
Fang &
Johanson(2005)
4,000
400
Windows
1.Dichotomous
PARDSIM
WinGen2
Yoes(1997)
Han (2007)
N/A
N/A
Windows
(16,32bit)
1.Dichotomous
100,000,000*
100,000,000*
Windows(32,64bit)
1.Dichotomous
2.Polytomous
3.Nonparametric
4.Multidimensional
Distribution
1.Uniform
1.Uniform
1.Uniform
1.Uniform
1.Uniform
1.Uniform
2.Normal
2.Normal
2.Normal
2.Normal
2.Normal
2.Normal
3.Lognormal
3.Lognormal
4.Two-Parameter Beta
4.Gamma
1.Replicating
Options
1.Replicating
1.Replicating
2.Introducing DIF/Drift
2.Multiple Blocks,
3.Communicating with
subtests, groups
other IRT software
4.Analyzing outputs
of other IRT software
5. Plotting ICF, TCC,
IIF, TIF, and histogram
of theta scores
6. Multiple tests,
groups.
* the maximum number of examinees and items could be more or less than 100,000,000; it mainly depends on the available system resources of
the computer on which WinGen runs.
Note: partially adopted from Harwell, Stone, Hsu, and Kirisci (1996, p.117)
II. Item Response Models Used within WinGen
Unidimensional IRT Models for Dichotomous Responses
Item response theory emerged as early as the 1940s though the popularity came much
later in the 1970s. As can be recognized by the name, IRT models consider examinee behavior at
the item level, not at the test level. Modeling at the item level creates much more flexibility for
applications to test development, study of differential item functioning, computer-adaptive
testing, score reporting, etc. Early IRT models were developed to handle dichotomous responses
(i.e., binary responses; for example, 0 (incorrect) and 1 (correct)) but today, models are available
to handle just about all types of educational and psychological data (see, van der Linden &
Hambleton, 1997).
User’s Manual: WinGen 11
Two of the fundamental assumptions with IRT models are unidimensionality and local
independence. The assumption of unidimensionality means that a set of items and/or a test
measure(s) only one latent trait (θ), and local independence refers to the assumption that there is
no statistical relationship between examinees’ responses to the pairs of items in a test, once the
primary trait measured by the test is removed. The two assumptions are really just different
ways to say the same thing about the data. The third main assumption concerns the modeling of
the relationship between the trait measured by the test and item responses. What follows are
various models that make different assumptions about that relationship.
Normal Ogive Model
The normal ogive model was the first IRT model for measuring psychological and/or
educational latent traits (Ferguson, 1942; Lawley, 1943; Mosier, 1940, 1941; Richardson, 1936).
The normal ogive model was refined later by Lord and Novick (1968). In the model, an item
characteristic curve (ICC) is derived from the cumulative density function (CDF) of a normal
distribution. A mathematical expression of the normal ogive model is as follows:
Pi ( )  
ai ( bi )

2
1 2z
e dz ,
2
(1)
where
Pi(θ) is the probability of a randomly chosen examinee at ability level θ answering item i
correctly,
ai is the discrimination parameter of item i,
bi is the difficulty parameter of item i, and
z is a standardized score of the examinee involving trait score, and the two item parameters.
One-Parameter Logistic Model (1PLM – a.k.a. Rasch Model)
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A mathematician in Denmark, George Rasch, came up with a different approach to IRT
in the 1950s (see, Rasch, 1960). He used a logistic function to derive an ICC instead of the
normal ogive function (though at the time he expressed his model differently), and his model
contributed to simplifying the normal ogive model and the complexity of computation, though at
the time, he appeared to be unaware of the earlier work on the topic of item response theory. In
the Rasch model, the probability of a randomly chosen examinee at an ability level θ obtaining a
correct answer on item i can be expressed as
Pi ( ) 
1
1  e  D ( bi )
,
(2)
where e is an exponential constant whose value is about 2.718, and D is a scaling factor whose
value is 1.7. The choice of this value for D, produces near equivalent values and interpretations
between the item parameters in the normal ogive and two-parameter logistic models. Today, it is
common to simply set D=1.0 since the normal ogive model is rarely used in practice and so
preserving consistent of interpretations between the models is not important. But it is important
to know when either studying item parameter estimates or generating them, that the value of D in
the model be considered. It is still common, especially with the two and three parameter logistic
models to retain D in the model with a value of 1.7. When D=1.0 (it is common to say that the
model parameters are placed on what is referred to as the “logistic metric”) and with D=1.7 (it is
common to say that the model parameters are placed on what is referred to as the “normal
metric”.)
Two-Parameter Logistic Model (2PLM)
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Two-parameter logistic model (2PLM) is a generalization of the 1PLM. Instead of having
a fixed discrimination of ‘1’ across all items as in 1PLM, in the 2PLM, each item has its own
discrimination parameter. Thus, the model is mathematically expressed as
Pi ( ) 
1
1 e
 Dai ( bi )
.
(3)
Three-Parameter Logistic Model (3PLM)
The three-parameter logistic model (3PLM) allows an ICC to have non-zero lower
asymptotes. This model is more suitable for response data with those items in which examinees
at the extremely low proficiency level may get the items correctly by chance; for example, a
multiple choice item. In this model
Pi ( )  ci  (1  ci )
1
1 e
 Dai ( bi )
,
(4)
where ci represents the probability that examinees at extremely low levels of the trait answer
item i correctly. This third item parameter, ci, is often called either the pseudo-chance-level
parameter or the guessing parameter, although ‘pseudo-chance-level parameter’ is theoretically
more appropriate (Hambleton, Swaminathan, & Rogers, 1991). The 2PLM is a special case of
3PLM when c=0, and 1PLM is a special case of 2PLM when a=1.
Nonparametric Item Response Model
ICCs are always characterized by a single function in IRT models with parameters.
However, assuming a single function for ICCs may not be appropriate to represent response data
in some cases. Nonparametric item response models, in which a variety of shapes of ICCs are
allowed, were developed in 1950s, even before parametric item response models were introduced.
User’s Manual: WinGen 14
Ramsay (1991) proposed a kernel smoothing approach for nonparametric item response
models. In a kernel smoothing approach, P(θ) is estimated at g-th evaluation point, qg, by a local
averaging procedure. Thus,
G
i ( )  w ( )Y ( g ) ,
P
 g i
(5)
g 1
when
wg ( ) 
K [(qg   ) / h]
 K [(q
k
  ) / h]
.
(6)
k
So,
 qg    ( g )
Yi
h

i ( )  g 
P
,
 qg   
g K  h 


K 
(7)
where
h is the bandwidth parameter, which controls bias and sampling variance, and
K(u) is one of the kernel functions (Ramsay, 1991, p.617):
(a) K(u)=0.5, |u|≤1, and 0 otherwise, for uniform,
(b) K(u)=0.75(1-u2), |u|≤1, and 0 otherwise, for quadratic, and
(c) K(u)=exp(-u2/2) for Gaussian.
Nonparametric item response models may not be as practically useful for operational uses
as parametric models because nonparametric item response models do not provide informative,
interpretable item parameters (for example, difficulty parameters), and it is hard to equate tests
under nonparametric models. However, nonparametric models are frequently used for research
User’s Manual: WinGen 15
purposes such as evaluating model fit for parametric models since nonparametric models
produce item characteristic fuctions that are very close to the observed data.
Unidimensional IRT Models for Analyzing Polytomous Responses
In dichotomous item response models, the only type of response data is binary (i.e., 0 or
1). However, in some test situations, responses can be of more than two categories. For example,
a questionnaire asking attitude, using Likert-scale items, may result in 5 categorical responses
(strongly disagree, disagree, neutral, agree, and strongly agree, which can be coded from 0 to 4).
Sometimes polytomous responses are dichotomized to be handled within dichotomous item
response models, but it is very inappropriate in most cases because dichotomizing polytomous
responses changes the nature of the scale of the measure and, as a result, validity of the measure
could be seriously threatened.
Several item response models were developed to enable uses of polytomous responses
within an IRT framework. Many of polytomous item response models are basically
generalizations of the dichotomous item response models.
Partial Credit Model (PCM)
The partial credit model is an extension of the 1PLM (a.k.a., Rasch model) (Masters;
1982, 1987, 1988a, 1988b). Equation (2) for the 1PLM above can be rewritten as
Pi ( ) 
1
1 e
 D ( bi )

exp( D (  bi ))
Pi1 ( )
,

1  exp( D (  bi )) Pi 0 ( )  Pi1 ( )
(8)
where Pi1(θ) is the probability of a randomly chosen examinee, whose proficiency level is θ,
scoring 1 on item i, and Pi0(θ) is the probability of a randomly chosen examinee, whose
User’s Manual: WinGen 16
proficiency level is θ, scoring 0 on item i. Thus, the probability of a person at θ, scoring x over x1 can be computed as
Pix ( )
exp( D(  bix ))

, x= 1, 2, …, mi,
Pix1 ( )  Pix ( ) 1  exp( D(  bix ))
(9)
where Pix(θ) and Pix-1(θ) refer to the probabilities of an examinee at θ, scoring x and x-1,
respectively. It should be noted that the number of item difficulty parameters are, now, mi (one
less than the number of response categories) in Equation (9). The probability of a randomly
chosen examinee, who is at θ, scoring x on item i can be expressed as
exp  k 0 ( D(  bik ))
x
Pix ( ) 

mi
h
exp  k 0 ( D(  bik ))
h
, x= 1, 2, …, mi.
(10)
The function of Equation (10) is often called the score category response function
(SCRF).
Generalized Partial Credit Model (GPCM)
The generalized partial credit model (Muraki, 1992) is a generalization of the PCM with
a parameter for item discrimination added to the model. Muraki (1992) expressed the model
mathematically as following:
exp  k 0 ( Z ik ( ))
x
Pix ( ) 

mi
h
exp  k 0 ( Z ik ( ))
h
,
(11)
where
Zik ( )  Dai (  bi  dix ) ,
(12)
where dix is the relative difficulty of score category x of item i. Although Muraki (1992) followed
the same way of parameterization for item and score category difficulty as Andrich’s (1978)
User’s Manual: WinGen 17
rating scale model, the item difficulty parameters for each score category can be simply rewritten
as
bix  bi  dix ,
(13)
Zik ( )  Dai (  bix ) .
(14)
and so is Equation (12),
The only difference between the PCM and GPCM is the additional discrimination parameters for
each item (ai). (In WinGen, the parameterization of Equation (14) is used.)
Rating Scale Model (RSM)
There are two different approaches to the rating scale model. Andersen’s (1977, 1983)
proposed a response function, in which the values of the category scores are directly used as a
part of the function:
Pix ( ) 
e wi aix

m
e
x 1
wx  aix
,
(15)
where w1,w2,…,wm are the category scores, which prescribe how the m response categories are
scored, and aih are item parameters connected with the items and categories. An important
assumption of this model is that the category scores are equidistant.
Another form of the RSM was proposed by Andrich (1978a, 1978b), which can be seen
as a modification of PCM. In Andrich’s RSM, item response functions are computed via
exp  j 0 (  (bi  dix ))
x
Pix ( ) 
 x0 (exp  j0 (  (bi  dij )))
m
x
.
(16)
User’s Manual: WinGen 18
where dix is the relative difficulty of score category x of item i. Andrich’s RSM assumes that the
category scores are fixed across all items in a testlet, and RSM should not be used if the scale of
category scores varies across items in a testlet. (In WinGen, Andrich’s RSM (Equation (16)) is
used, and d- parameters are renamed to c- in the program interface only for an operational
reason.)
Graded Response Model (GRM)
The graded response model was introduced by Samejima (1969, 1972, 1995) to handle
ordered polytomous categories such as letter grading, A, B, C, D, and F and polytomous
responses to attitudinal statements (such as a Likert scale). The model is expressed as
Pix* ( ) 
exp( Dai (  bix ))
,
1  exp( Dai (  bik ))
(17)
where P*ix(θ) is the probability of an randomly chosen examinee with proficiency of θ scoring x
or above on item i. This function is called the cumulative category response function (CCRF).
Probability of each score category can be given by
Pix ( )  Pix* ( )  Pix*1 ( ) .
(18)
Thus, the score category response function (SCRF) of the GRM can be expressed as
Pix ( ) 
exp[ Dai (  bix1 )]  exp[ Dai (  bix )]
.
[1  exp[  Dai (  bix )]][1  exp[ Dai (  bix1 )]]
(19)
Unlike the PCM and GPCM, the interpretation of item parameters of the GRM should be based
on the CCRF, not on the SCRF. Within the GRM, a value of b-parameter for each response
category indicates where a probability that a randomly chosen examinee, whose proficiency level
(θ) is exactly same as the value of b-parameter, scores x or higher is 50% on the CCRF.
User’s Manual: WinGen 19
Although the statistical approaches to category response functions are totally different
between the GRM and GPCM (Equation (11)), and so are the interpretation of item parameters,
the SCRFs from the two models are usually very close to each other.
Nominal Response Model (NRM)
The nominal response model (also called the Nominal Categories Model) was introduced
by Bock (1972). Unlike the other polytomous IRT models introduced above, polytomous
responses in NRM are unordered (or at least not assumed to be ordered). Even though responses
are often coded numerically (for example, 0,1,2,…,m), the values of the responses do not
represent some sort of scores on items, but just nominal indications for response categories.
Some applications of the NRM are found in uses with multiple choice items. The category
function of NRM can be expressed as
Pix ( ) 
e zix
mi
e
,
zik
(20)
k 1
where
zix  aix  bix .
(21)
In Equation (21), aix and bix are called the slope and intercept parameters, respectively, and they
are related with item discrimination and location. The sum of a- parameters and the sum of bparameters across response categories are constrained to be zero.
.
Multidimensional IRT Model for Dichotomous Responses
Multidimensional Compensatory Three-Parameter Logistic Model (MC3PLM)
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Whether it is intended or not, when an item or a set of items measures more than one
latent trait, the assumption of unidimensionality is violated. The violation of the
unidimensionality assumption may cause a systematic bias in the measurement process even
though unidimensional IRT models are known to be somewhat robust against this violation.
Reckase (1985) came up with a multidimensional IRT model which can be seen as an
extension of the unidimensional 3PL model:
e( a 'i  bi )
Pi ( )  ci  (1  ci )
,
1  e( a 'i  bi )
(22)
where
Pi(θ) is the probability of a correct response on test item i for a randomly chosen examinee
whose proficiency is θ,
ai is a vector of parameters related to the discriminating power of the test item,
bi is a parameter related to the difficulty of the test item (but, NOT the difficulty itself),
ci is a pseudo-chance level parameter, and
θ is a vector of trait scores for the examinee on the dimensions.
Equation (22) is very similar to the 3PLM (Equation (4)) except the fact that ai and θ are vectors
of the parameters for each dimension. A vector of a-parameters in Equation (22) can be
tranformed to
MDISCi 
p
a
k 1
2
ik
,
(23)
where MDISCi is the discrimination of the item i for the best combination of abilities and p is the
number of dimensions. Also, a value that is equivalent in interpretation to the unidimensional bparameter can be given by
User’s Manual: WinGen 21
MDIFFi 
bi
.
MDISCi
(24)
User’s Manual: WinGen 22
III. Quick Start
Generating Examinee Data (Step 1)
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 a green ‘Generate’ button
⑤ Generated examinee theta scores should be shown in the box. The data set can be saved at
‘File > Save > Examinee Data’
User’s Manual: WinGen 23
⑥ Distribution of examinee thetas can be shown by clicking on the ‘Histogram’ button.
An example of generating examinee data where 50,000 examinees were drawn from a
beta distribution (a=2, b=4) is shown in Figure 3.1. The use of beta distributions makes it easy to
simulate skewed score distributions.
Figure 3.1 Example of Generating Examinee Data
User’s Manual: WinGen 24
Generating Item Data (Step 2)
① Specify the number of items
② Specify the number of response categories. Select ‘2’ for dichotomous response data.
③ Select an IRT model
④ Select distribution of item parameters and specify properties of the distributions
⑤ Click on a red ‘Generate’ button
⑥ Generated item parameter data should be shown in the box. The data set can be saved at
‘File -> Save -> Item Parameter Data’
⑦ Item Characteristic Curves (ICCs), Test Characteristic Curve (TCC), Item Information
Function Curves (IIF), and Test Information Function Curve (TIF) are provided by
clicking on the ‘IRT Plots’ button
User’s Manual: WinGen 25
⑧ Mark the check box, ‘Add to the previous item set’, and repeat steps (① to ⑦) if another
set of items (or items of different IRT models) needs to be added to a previous set of
items. This option is particularly useful when a mixed format test form is to be simulated.
An example of generating item data, where 15 dichotomous items based on 3PLM and 5
polytomous items based on GRM (5 categories) are generated, is shown in Figure 3.2.
Figure 3.2 Example of Generating Item Data
User’s Manual: WinGen 26
Generating Item Response Data (Step 3)
① Make sure examinee data generated in Step1 or a data set is opened with the pull-down
menu, ‘File > Open > Examinee Data’
② Make sure item parameter data generated in Step2 or a data set is opened with the pulldown menu, ‘File > Open > Item Parameter Data’
③ Specify the name of the response data file by clicking on ‘Browse’
④ Check the check box and specify the number of replications if replication data are desired
⑤ Adjust options at ‘Tools -> Options’
⑥ Click on the blue ‘Generate Response Data Set(s)’ button. The data set should be seen by
opening up the file with the extension of ‘.wgr’
User’s Manual: WinGen 27
An example of generating item data, where 15 dichotomous items based on the 3PLM
and 5 polytomous items based on the GRM (5 categories) are generated, is shown in Figure 3.3.
Figure 3.3 Example of Simulating Response Data
User’s Manual: WinGen 28
Options
‘Scale to normal metric (scaling factor, D=1.7)’ (default: unchecked). By checking this
option, WinGen generates item response data on the same scale as the normal-ogive model.
Even when the normal ogive model though is of little interest, it is common to report scores
on the “normal metric.” This is less true when the polytomous response models are used.
‘Specify SEED values for generating data’ (default: unchecked). If it is unchecked, WinGen
will set SEED values according to a system clock.
If Option
is checked, three SEED values have to be specified for examinee data, item
parameter data, and item response data, respectively. Specifying SEED values enables users
to have control over generating random numbers.
‘Display only the first 5,000 examinees in the main page’ (default: checked). WinGen
displays only first 5,000 examinees in the main page if this option is checked. Undisplayed
examinees are still in the memory and will be used for plotting a histogram and for
User’s Manual: WinGen 29
simulating response data. All examinees can be displayed by unchecking this option, but it
may significantly slow down the processing time.
‘Generate input files for estimating program’ (default: checked). This option allows WinGen
automatically generating syntax files for estimating software, such as PALSCALE, BilogMG, and MULTILOG.
If Option
is checked, an estimating program has to be selected. Automated syntaxes for
PARSCALE and for Bilog-MG are written to estimate parameters based on the 3PLM, and
automated syntaxes for MULTILOG are written to estimate parameters based on the 2PLM.
‘Read in a sample input file’ (default: unchecked). If it is checked, users can import a sample
syntax file for an estimating program and make WinGen generate automated syntax based
on the sample file imported. It must be noted that there should be one statement/command
per line in a sample file.
If Option
is checked, a sample input file for an estimating program has to be specified.
The sample input file specified should be for the estimating program chosen at Option
.
‘Generate a batch file’ (default: checked). If it is checked, WinGen automatically generates a
batch file by which users or WinGen can run estimating programs by one cue.
‘Automatically run a batch process’ (default: unchecked). If it is checked, WinGen will
automatically run a batch file to run estimating programs after simulating data.
‘Analyze item parameter estimates’ (default: unchecked). If it is checked, WinGen will
import item parameter estimates from the estimating program chosen above and calculate
the correlation, RMSE(RMSD), MAD, and BIAS. The statistics computed are stored in
‘*.wgz’ files.
⑫ ‘Analyze trait (theta) estimates’ (default: unchecked). If it is checked, WinGen will import
examinee score estimates from the estimating program chosen above and calculate the
correlation, RMSE(RMSD), MAD, and BIAS. The statistics computed are stored in ‘*.wgz’
files.
User’s Manual: WinGen 30
VI. WinGen Files
File Extensions
WinGen uses and produces several kinds of input and output files. Unique extensions are
assigned on files according to their purposes. The files associated with WinGen are summarized
in Table 4.1.
Table 4.1 Extensions of WinGen Files
Extension
Description
Type
*.wgc
WinGen cue file for executing sets of syntax files
Input only
*.wgd
WinGen descriptive statistics for simulated data (examinee, item)
*.wge
WinGen data file for Examinees
Input and Output
*.wgi
WinGen data file for Item Parameters
Input and Output
*.wgr
WinGen data file for Generated Responses
*.wgs
WinGen syntax file
*.wgz
WinGen analysis summary file
*.blm
Bilog-MG syntax file
Input and Output
*.psl
PALSCALE syntax file
Input and Output
*.mlg
MULTILOG syntax file
Input and Output
*.par
Item parameter data file for Bilog-MG, PALSCALE, or MULTILOG
Output only
*.sco
Examinee score data file for Bilog-MG, PALSCALE, or MULTILOG
Output only
Output only
Output only
Input only
Output only
WinGen File Formats
All input and output files of WinGen are ASC text file format, which can be opened and
edited by Notepad, TextPad, MS Excel, SPSS, SAS, so on.
(a) WinGen Examinee data file (*.wge) – ‘tab-delimited’
Format: [ID][theta’s]
User’s Manual: WinGen 31
(b) WinGen Item parameter data file (*.wgi) – ‘tab-delimited’
Format: [Item#][Model][# of categories][a-parameters][b-parameters][c-parameters]
Models: 1PLM, 2PLM, 3PLM, NON, GRM, PCM, GPCM, NRM, RSM, and/or MC3PLM
User’s Manual: WinGen 32
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
MC3PLM: Multidimensional Compensatory Three Parameter Logistic Model
NON: Non-Parametric Model
NOTE: When the non-parametric model is used, another format should be used as following:
[Item#][‘NON’][# of evaluation points between -3.0 and 3.0 on the theta scale][list of
probabilities for each evaluation point]
(c) WinGen item Response data file (*.wgr) – ‘space-delimited’
Format: [Examinee ID][2 spaces][Response string]
User’s Manual: WinGen 33
Naming Rules for Simulated Response Data Files
When a user generates more than one replication of the data and/or generates DIF/IPD
data, WinGen automatically modifies the response data file name to organize a set of response
data files generated. The naming rules WinGen uses are summarized in Table 4.2.
Table 4.2 Naming Rules for Response Data Files
Modified File Name
Explanation
filename
a single data set
filename_1, filename_2, …, filename_n
n sets of replicated data
filename_r
a single data set for a reference group in
DIF/IPD study
filename_f
a single data set for a focal group in DIF/IPD
filename_r_1, filename_r_2, …, filename_r_n
n sets of replicated data for a reference group in
DIF/IPD study
filename_f1_1, filename_f1_2, filename_f2_1, n sets of replicated data for m-th focal group
filename_f2_2, …, filename_fm_n
* the file extension for response data files, ‘*.wgr’, is skipped in the table
User’s Manual: WinGen 34
V. Advanced Uses of WinGen
Generating Response Data with DIF / IPD
There are two ways for generating response data with DIF/IPD: (a) direct input mode,
and (b) multiple file read-in mode.
(a) Direct Input Mode
User’s Manual: WinGen 35
NOTE: Direct Input Mode supports only the 1PLM, 2PLM, and 3PLM. In order to introduce
DIF/IPD on the items with other models, Multiple File Input Mode should be used.
① Make sure examinee data generated in Step1 or a data set is opened at
‘File>Open>Examinee Data’
② Make sure item parameter data generated in Step2 or a data set is opened at
‘File>Open>Item Parameter Data’
Then, select items that are to be with DIF/IPD
③ Click on ‘DIF/IPD’ tab
④ The items selected at
should be shown in the box. Select an item to introduce DIF/IPD
on the item
The original parameters of the item selected should be in the first column. Specify either
item parameter with DIF/IPD in the second column or the amount of DIF/IPD in the third
column
User’s Manual: WinGen 36
Click on ‘Update’ button. The amount of DIF/IPD should be reflected In the box of
on the process of
,
, and
. Go
for all the items to which you want to introduce DIF/IPD
Click on ‘Main’ tab
Specify the name of response data file by clicking on ‘Browse’
Check the check box and specify the number of replications if replicated studies are
desired
Adjust Options at ‘Tools>Options’
Click on the blue ‘Generate Response Data Set(s)’ button. The data set should be seen by
opening up the file with the extension of ‘.wgr’
(b) Multiple File Read-in Mode
User’s Manual: WinGen 37
Click on ‘DIF/PD’ tab
Click on the radio button in the bottom (‘Introduce DIF/IPD via Multiple File Read-in
Mode)
Click on ‘Browse’ button and specify an examinee data file for a reference group
Click on ‘Browse’ button and specify an item parameter data file for a reference group
Click on ‘Browser’ button and specify an examinee data file for all focal groups
Or, specify examinee data files exactly as many as the number of focal groups
Specify item parameter data files exactly as many as the number of focal groups
Click on ‘Main’ tab
Specify the name of response data file by clicking on ‘Browse’
Check the box and specify the number of replications if replicated studies are desired
Adjust Options at ‘Tools > Options’
Click on the blue ‘Generate Response Data Set(s)’ button. The data set should be seen
by opening up the file with the extension of ‘.wgr’
User’s Manual: WinGen 38
Generating Multidimensional Item Response Data
User’s Manual: WinGen 39
① Specify the number of examinees
② Select type of score distribution
③ Specify mean and standard deviation for the normal distribution
or, specify minimum and maximum value for a uniform distribution
or, specify a and b parameters for a beta distribution
④ Click on the checkbox, ‘Multidimensional’. A Dialog box will pop up.
⑤ Select the number of dimensions (up to 5)
⑥ Select type of distribution and specify the characteristics of the distribution for each
dimension. Dimensions 2 to 5 can be set to be correlated with the dimension 1 by
selecting ‘Correlated’. Click on ‘OK’ button.
⑧ Specify the number of items. The number of response categories is automatically set to ‘2’
since in this version of WinGen only dichotomous response data can be simulated. The
model is automatically set to ‘MC3PLM’.
Select distribution of item parameters and specify properties of the distributions
Click on the red ‘Generate’ button
Specify the name of the response data file by clicking on ‘Browse’
⑫ Click on the blue ‘Generate Response Data Set(s)’ button. The data set can be seen by
opening up the file with the extension of ‘.wgr’
Using Syntax Files and Cue Files
A user can use a syntax file to run WinGen instead of point-and-click on the graphic
interface. Syntax files for WinGen can be composited using any kind of text editor software such
as ‘Notepad’ or ‘TextPad’.
Table 5.1 Commands / Options Used in the WinGen Syntax File
Line / Description
Line1.
Examinee Data
Characteristics
Commends / Options
[# of examinees],
[type of distribution],[mean/min/a],[SD/max/b],[‘replicate’ or
nothing]
User’s Manual: WinGen 40
* ‘skip’ option lets WinGen skip
generating examinees’ data, and
WinGen will use examinees’ data
which currently is loaded in the
examinees’
theta
box
for
simulating the response data.
Line2.
Item Data Characteristics
* ‘skip’ option lets WinGen skip
generating item parameters, and
WinGen will use item parameter
data which currently is loaded in
the item parameter box for
simulating the response data.
[‘skip’]
[‘file’],[full filename of the examinee data (*.wge) including the
path (the name of the folder)]
[‘MIRT’],[# of examinees],[# of dimensions],[‘replicate’ or
nothing]
Followed by
[distribution for the first dim.],[mean/min/a],[SD/max/b]
[distribution for the second dim.],[mean/min/a],[SD/max/b]
……
[# of items],[# of response categories],[model],[distribution for
item parameter],[mean/min/a],[SD/max/b],….
[‘skip’]
[‘file’],[full filename of the item data (*.wgi) including path the
(the name of the folder)]
Line3.
[full name of the response data (*.wgr) including the path where
Name of Response Data File the simulated response data will be saved]
Line4.
[’replication’],[# of replications if you chose ‘replication’]
Replication
[‘1’]
Line5.
Scale (Normal or Logistic)
[’logistic’]
[‘normal’]
Line6.
Seed Value
[’random’]
Line7.
Programs for
Estimating Parameters
[’none’]
[‘Bilog-MG’ or ‘Parscale’ or ‘Multilog’],[‘auto’]
[‘Bilog-MG’ or ‘Parscale’ or ‘Multilog’],[full filename including
the path of the sample syntax file for the program]
* ’auto’ option can be used only
for dichotomous response data
sets.
[SEED for examinees],[SEED for items],[SEED for responses]
Line8.
[’none’]
A Batch to Run Programs
for Estimating Parameters
[‘batch’]
* the option ‘batch’, ‘run’, ‘item’,
and ‘score’ trigger the options of
[‘batch’],[‘run’]
User’s Manual: WinGen 41
, , , and
in the Option
dialog. See Section 4. ‘Options’
above for details.
[‘batch’],[‘run’],[‘item’]
[‘batch’],[‘run’],[‘item’],[‘score’]
* The commands/options italicized are the places where your inputs need to be placed.
** The commands/options in quotation marks are the actual commands/options to be input except the quotation
marks.
*** Each line of syntax is delimited by a comma (’,’). There should be no space before and after the comma.
Example #1: 3,000 examinees and 50 items with 2PLM
WinGen will generate 3000 theta scores from a normal distribution with a mean of 0 and
a standard deviation of 1. Then, WinGen will generate 50 items with 2PLM (‘a’ parameters from
a lognormal distribution with a mean of 0 and a SD of 0.5, and. ‘b’ parameters from a normal
distribution with a mean of 0 and a SD of 1). WinGen will store simulated response data into
‘d:\templap\responses1.wgr’ WinGen does not replicate data (i.e., just simulate data one time).
The response data will be simulated based on the logistic model scale (D=1.0). SEED values will
be randomly chosen. WinGen will not generate syntax files for the programs for estimating
parameters and WinGen will not generate a batch file, according to the specifications of the user.
Example #2: Reading-in examinee and item data from files
User’s Manual: WinGen 42
WinGen will read-in examinees’ data from the file named ‘d:\templab\sample.wge’ Then,
WinGen will read-in item parameter data from ‘d:\templab\sample.wge’ WinGen will store
simulated response data into ‘d:\templap\responses2.wgr’ WinGen does not replicate data (i.e.,
just simulate data one time). The response data will be simulated based on the logistic model
scale (D=1.0). SEED values will be 102134, 23,213421 for examinees, items, and responses,
respectively although SEED values for examinees and items will not be used since the user had
WinGen read-in from files . WinGen will not generate syntax files for the programs for
estimating parameters and WinGen will not generate a batch file, according to the specifications
of the user.
Example #3: Generating examinees, using existing items in memory, replicating, and estimating
WinGen will generate 5000 examinee theta scores from a beta distribution with the
distribution parameters of 1 and 3. Then, WinGen will read-in item parameter data from
‘d:\templab\sample.wge’
WinGen
will
store
simulated
response
data
into
‘d:\templap\responses3.wgr’ (actually, the response files will be saved with the name of
User’s Manual: WinGen 43
‘reponse3_1.wgr’,
‘reponse3_2.wgr’,
‘reponse3_3.wgr’,
‘reponse3_4.wgr’,
and
‘reponse3_5.wgr’ since you have a syntax for replicating this study 5 times). The response data
will be simulated based on normal metric scale (D=1.7). SEED values will be randomly chosen.
WinGen will generate syntax files for PARSCALE automatically (not from a sample code), and
will generate a batch file to run PARSCALE for the 5 replications. PARSCALE will estimate
only the item parameters.
Example #3: Simulating multidimensional IRT data (2 dimensions)
WinGen will generate 3000 examinees’ theta for two dimensions. The first theta
distribution will be drawn from a uniform distribution between –3 and 3. The vector of theta for
the second dimension will be correlated with the first dimension of theta. Then, 20 items with
MC3PLM will be generated (a-parameters from a lognormal distribution, b-parameters from a
normal distribution, and c-parameters from a beta distribution). WinGen will store simulated
response data into ‘d:\templap\responses4.wgr’. WinGen will not replicate this study. The
response data will be simulated based on logistic model scale (D=1.0). SEED values will be
randomly chosen. WinGen will not generate syntax files for the programs for estimating
parameters. WinGen will not generate a batch file.
Cue File
A cue file is kind of a batch file with which WinGen runs multiple syntax files. It is simply a list
of full file names of the syntax files. A cue file can be executed at “File>Open and Run> Cue
File” on the menu bar.
User’s Manual: WinGen 44
Example of a Cue File
User’s Manual: WinGen 45
References
Baker, F. B. (1989). GENIRV: A program to generate item response vectors (Unpublished
manuscript). Madison, WI: University of Wisconsin, Laboratory of Experimental
Design.
Fang, H., & Johanson, G. (2005, April). WINIRT: A Windows-based item response theory data
generator with an equating and differential item functioning simulation guide. Paper
presented at the meeting of the American Educational Research Association, Montreal,
Canada.
Hambleton, R. K., & Rovinelli, R. (1973). A Fortran IV program for generating examinee
response data from logistic test models. Behavioral Science, 17, 73-74. (Software was
revised, September 1990)
Hambleton, R. K., Swaminathan, H., & Rogers, H. J. (1991). Fundamentals of item response
theory. Newbury Park, CA: Sage.
Han, K. T. (2007). WinGen2: Windows software that generates IRT parameters and item
responses [computer program]. Amherst, MA: University of Massachusetts, Center for
Educational
Assessment.
Retrieved
May
13,
2007,
from
http://www.umass.edu/remp/software/wingen/
Harwell, M. R., Stone, C. A., Hsu, T.-C., & Kirisci, L. (1996). Monte Carlo studies in item
response theory. Applied Psychological Measurement, 20(2), 101-125.
Microsoft. (2002). Microsoft Windows XP [computer program]. Redmond, WA: Author.
Microsoft. (2005). Microsoft .NET framework version 2.0 [computer program]. Redmond, WA:
Author.
Muraki, E. (1992). RESGEN: Item response generator [computer program]. Princeton, NJ:
Educational Testing Service.
Muraki, E., & Bock, R. D. (2003). PARSCALE 4: IRT item analysis and test scoring for ratingscale data [computer program]. Chicago, IL: Scientific Software.
Thissen, D. (2003). MULTILOG 7: Multiple categorical item analysis and test scoring using item
response theory [computer program]. Chicago, IL: Scientific Software.
Yoes, M. (1997). PARDSIM [computer program]. St. Paul, MN: Assessment Systems
Corporation.
User’s Manual: WinGen 46
van der Linden, W. J., & Hambleton, R. K., (Eds.). (1997). Handbook of modern item response
theory. New York: Springer-Verlag.
Zimowski, M. F., Muraki, E., Mislevy, R. J., & Bock, R. D. (2003). BILOG-MG 3 [computer
program]. Chicago, IL: Scientific Software.
Version: May 13, 2007
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