ETIRM: Estimation Toolkit for Item Response Models

Download | Documentation | Examples | Requirements | Configuration

Werner Wothke

Release: 080301 (March 1, 2008)

ETIRM is a set of C++ classes and functions for parameter estimation of item response theory (IRT) models. Currently, the components of ETIRM can be used to compute estimates of the three-parameter logistic model for dichotomous items (including the one-parameter and two-parameter logistic models as special cases), and the generalized partial credit model for polytomous items (including the partial credit model as a special case). Parameter estimation is supported when groups of examinees that are not randomly equivalent take different sets of items, with some items in common between the sets (multiple-group estimation). One situation in which such data would arise is in the common-item nonequivalent groups equating design. Besides estimation of item parameters, ETIRM can be used to estimate latent variable distributions for groups, and latent variable values for individual examinees. ETIRM can also be used for simulating item responses from one of the supported IRT models. ETIRM is free software distributed under the BSD License.

ETIRM is a C++ toolkit for building IRT estimation programs, it is not itself a program for computing IRT parameter estimates. A stand-alone program has been created using ETIRM for multiple group estimation of dichotomous and polytomous IRT models - IRT Command Language (ICL). In addition, the source code for several simple programs created using ETIRM are included in the ETIRM distribution. The example programs, as well as the source code for ICL, illustrate how to use ETIRM to create a program.

ETIRM was developed by Brad Hanson (2000-2002) and was originally managed through the SourceForge website as part of the Social Science Measurement project. A more recent update of the ETIRM code and documentation by Werner Wothke (2008) is now hosted on this website.

Some knowledge of C++ and a C++ compiler are necessary to create a program using ETIRM. Free C++ compilers are available for Windows NT/2000/XP/Vista including the Borland 5.5 compiler and Cygwin (including the gcc compiler). Some of these compilers also run on Windows 95/98/ME platforms. Linux includes the gcc compiler.

Programs using ETIRM have been successfully compiled with the CodeWarrior 6.2 compiler on Mac OS and Windows NT, the gcc 3.4.4 on Windows Vista, gcc 2.95.2 compiler on Linux, and the Borland 5.5 compiler on Windows. There may be some problems in using ETIRM with compilers that are less compliant with the C++ standard. For example, when using ETIRM with Visual C++ 6 it is recommended that the Boost library configuration system be used (see the configuration section below for details).

Download and Install

Download ETIRM - Zip archive containing ETIRM. The archive contains a single directory named 'etirm' holding the ETIRM source files. See the README file for information about the files included in the archive. The source files in this archive are stored with DOS line breaks (the files are DOS text files).

It is suggested to unpack the zip archive into the C:\programs\etirm folder, into the sub-folders src, lib, doc, examples, and webpage, respectively. The gcc/cygwin makefiles included in the zip-archive were prepared for this folder convention.

Documentation

The documentation for ETIRM consists of this file as well as comments in the source files. The source file comments were written to be compatible with the doxygen documentation system. The on-line source code documentation contains descriptions of each file, class, and function that are part of ETIRM. This documentation is also contained in the doc directory of the ETIRM distribution.

Some documentation of the numerical algorithms used in ETIRM is provided in Woodruff and Hanson (1997) and Hanson (1998). These documents describe the algorithms used in ETIRM for single group estimation. These documents do not provide a complete description of the algorithms used in ETIRM since they do not cover multiple group estimation.

ETIRM Source Files

ETIRM consists of a number of C++ classes and functions. The goal was to make the individual components of ETIRM as independent as possible, so that the components could be used individually with minimum dependence on other components of ETIRM. C++ templates are heavily used in ETIRM to facilitate this independence.

The following are brief descriptions of the source files in ETIRM. Some source files in the list are nested within other source files. A nested source file declares or defines a class derived from the class declared or defined in the file it is nested under.

• BootstrapSample.h - Definition of function BootstrapSample for generating a bootstrap sample.
• DiscreteLatentDist.h - Definition of class DiscreteLatentDist representing a discrete latent variable distribution for one or more groups of examinees.
• DiscreteNormalDist.h - Definition of function DiscreteNormalDist for computing points and probabilities for a discrete distribution that approximates a normal distribution.
• EStepDiscrete.h - Definition of class EStepDiscrete which can be used in performing the E-step calculation of the EM algorithm for item response models.
• etirmtypes.h - Defines some basic types used in ETIRM.
• Examinee.h - Definition of class Examinee which holds item responses for an examinee.
  • ExamineeGrpCov.h - Definition of class ExamineeGrpCov that includes information about the group the examinee belongs to.
• ExamineeThetaMLE.h - Definition of the ExamineeThetaMLE function for computing a maximum likelihood estimation of the latent variable value for an examinee.
• ICCLogistic.h - Definitions of specializations of template class ICCLogistic for computing item characteristic curves for 1, 2, and 3 parameter logistic models for dichotomous items.
• ICCLogistic.cpp - Definitions of non-template member functions declared in ICCLogistic.h.
• ICRF_GPCM.h - Definition of class ICRF_GPCM for computing item category response functions for the generalized partial credit model.
• ICRF_GPCM.cpp - Definitions of member functions for ICRF_GPCM class.
• ICRF_PCM.h - Definition of class ICRF_PCM for computing item category response functions for the partial credit model.

• ICRF_PCM.cpp - Definitions of member functions for ICRF_PCM class.

• Item.h - Definition of abstract class Item which stores information about a test item.
  • ItemNR.h - Definition of class ItemNR which includes information calculated for the item in the E-step (n's and r's) which is used in the M-step.
    • ItemDichotomous.h - Definition of class ItemDichotomous representing a dichotomously scored item.
    • ItemPolytomous.h - Definition of class ItemPolytomous representing a polytomously scored item.
• ItemParamPrior.h - Definition of abstract class ItemParamPrior which represents a prior distribution for item parameters.
  • ItemParamPriorBeta4.h - Definition of class ItemParamPriorBeta4 representing a four-parameter beta prior distribution.
  • ItemParamPriorLogNormal.h - Definition of class ItemParamPriorLogNormal representing a lognormal prior distribution.
  • ItemParamPriorNormal.h - Definition of class ItemParamPriorNormal representing a normal prior distribution.
• ItemParamPrior.cpp - Definitions of member functions for class ItemParamPrior.
  • ItemParamPriorBeta4.cpp - Definitions of ItemParamPriorBeta4 member functions.
  • ItemParamPriorLogNormal.cpp - Definitions of ItemParamPriorLogNormal member functions.
  • ItemParamPriorNormal.cpp - Definitions of ItemParamPriorNormal member functions.
• MStepIRT.h - Definitions of template functions used to compute the M-step for item parameter estimates and estimates of the probabilities of discrete latent variable distributions.
• MStepIRT.cpp - Definition of function MaxRelParamDiff used in M-step calculations.
• Start3PL.h - Definitions of functions used to compute starting values for the one, two, or three-parameter logistic models.
• SimulateResponses.h - Definition of function SimulateResponses that returns simulated item responses for a latent variable value.
• swig_etirm.cpp - Definitions of functions and classes to be wrapped by SWIG to create scripting language interfaces for ETIRM.
• swig_etirm.h - Declarations of functions and classes to be wrapped by SWIG to create scripting language interfaces for ETIRM. This file would be included in a SWIG interface file to create the wrappers for the functions defined in swig_etirm.cpp.
• swig_etirm_types.h - Definition of basic types referenced by swig_etirm.h.
• ThetaLogLikelihood.h - Definition of function object ThetaLogLikelihood for computing the log of the likelihood for an examinee theta parameter in a item response model.

Building the ETIRM Link Library

A makefile in the LIB sudirectory can be used to build the libetirm.a link library with gcc and cygwin. The makefile is easily modified to accomodate different development environments.

Examples

Example programs using ETIRM are provided in the examples directory of the ETIRM distribution. There are four example programs provided. Each program is contained in a subdirectory within the examples directory:

• one_group - Item parameter estimation program for the three-parameter logistic model assuming all examinees are sampled from a single population (single group estimation).
• two_groups - Item parameter estimation program for the three-parameter logistic model in the case in which two forms with some common items are taken by two groups sampled from different populations (multiple group estimation).
• simpoly - Program which simulates item responses for a test with 60 dichotomous items modeled using the three-parameter logistic model, and 4 polytomous items modeled using the generalized partial credit model.
• one_group_poly - Item parameter estimation program that allows a mix of dichotomous items modeled by the three-parameter logistic model, and polytomous items modeled by the generalized partial credit model. All examinees are assumed to come from a single population in the case in which all examinees do not take the same items.

Included with the programs are makefiles for compiling the programs using gcc under Windows (Makefile). The first two programs include makefiles for compiling the program with the Borland 5.5 compiler (Makefile.win) on Windows 95/NT, although these files are not being maintained and may need some modification to work with the current version of ETIRM. The information in these makefiles can be used to compile the program using other compilers.

Requirements

External classes for minimization and classes implementing vectors and matrices are required by ETIRM. These classes are used in ETIRM as typedefs or template arguments, so any classes that meet certain interface requirements can be used. Two C++ packages that can be used with ETIRM to fulfill these requirements are:

• Uncmin++ - Includes the Uncmin unconstrained minimization class (used in the M-step computation), and the Fmin function used by ExamineeThetaMLE. The current release of Uncmin++ is 080309.
• Simple C++ Numerical Toolkit (SCPPNT) - Provides vector and matrix classes, and operations on vectors and matrices. The current version of SCPPNT is 071218.

SCPPNT, or another vector and matrix package with the same interface, must be available to compile programs that use ETIRM. Uncmin++, or another minimization package having the same interface, is required for some components of ETIRM. If a vector and matrix package other than SCPPNT is used then the files etirmtypes.h and swig_etirm.h will need to be modified. If a minimization package other than Uncmin++ is used, then the files swig_etirm.h and ExamineeThetaMLE.h will need to be modified. This version of ETIRM has been successfully used with release 0.011002 of Uncmin++ and version 0.010516 of SCPPNT.

The BootstrapSample function in BootstrapSample.h and the SimulateResponses function in SimulateResponses.h require a function object generating random numbers. Random number classes from the Boost C++ library (version 1.26.0 or later) meet the requirements for these functions. The Boost library is also used in etirm_swig.h. In addition, the example program in the simpoly directory shows how to use Boost random number objects with the SimulateResponses function.

The ExamineeThetaMLE function in ExamineeThetaMLE.h uses the Fmin function for univariate minimization. The Fmin function is contained in the file Fmin.h, which is included with Uncmin++ release 080302 or later.

When building the example programs with some older, not quite standard-compliant compilers, the STLport library may have to be linked in. With the current version of the cygwin toolchain (1.5.25-7), a separate STLport library is no longer required.

Configuration

• ETIRM_NO_DIR_PREFIX - Unless this symbol is defined included ETIRM header files are prefixed by the directory name 'etirm'. For example, if this symbol is not defined the header etirmtypes.h would be included using #include "etirm/etirmtypes.h", as opposed to #include "etirmtypes.h" if this symbol is defined.
• ETIRM_FLOAT_TYPE - Defines the type used to represent floating point numbers in ETIRM. This symbol is used in etirmtypes.h. By default ETIRM_FLOAT_TYPE is defined to be double.
• ETIRM_RESPONSE_TYPE - Defines the type used to represent examinee item responses. This symbol is used in etirmtypes.h. By default ETIRM_FLOAT_TYPE is defined to be char.
• ETIRM_USE_BOOST_CONFIG - Use the Boost library configuration system to control the definitions of Boost symbols used by ETIRM (see below). When
• ETIRM_USE_BOOST_CONFIG is defined some ETIRM source files include the Boost configuration file config.hpp. (Note: In the cygwin envirionment, these "BOOST" symbols are no longer necessary, provided that the cygwin boost folder is added to the gcc include search path, as demonstrated in the make files).
• SCPPNT_BOUNDS_CHECK - Use this symbol to request runtime index checking in SCPPNT routines.
• SCPPNT_NO_DIR_PREFIX - This symbol requires SCPPNT include (*.h) files to be stored in the same directory as the CPP files.

ETIRM uses some symbols from the Boost library configuration system. These symbols begin with BOOST_. These symbols can be manually defined without using the Boost library (when ETIRM_USE_BOOST_CONFIG is not defined). Alternatively, if ETIRM_USE_BOOST_CONFIG is defined then the Boost library is assumed to be available and whether these symbols are defined or not is determined by the Boost configuration system for the particular compiler being used.

• BOOST_NO_STDC_NAMESPACE - Define if functions from the standard C library are not put in the std name space.
• BOOST_MSVC6_MEMBER_TEMPLATES - Define if the compiler does not allow member templates to be defined outside the class definition (like Microsoft Visual C++ version 6).
• BOOST_MSVC - Define if Microsoft Visual C++ version 6 is being used.
• BOOST_NO_LIMITS - Define if the <limits> header from the standard C++ library is not available.

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Last updated: November 18, 2014