Equating Software for the Multiple-Choice Model

Bradley A. Hanson

Release: 0.000408 (April 8, 2000)

This software performs item response theory (IRT) equating using the characteristic curve method for the multiple-choice and the nominal response models as described in Kim and Hanson (2000). Specifically, the software computes a linear transformation to convert parameter estimates on one scale (denoted the current scale) to another scale (denoted the target scale). This software was written for the purpose of illustrating the procedures described in Kim and Hanson (2000). There are some significant limitations of the software (all items must have the same number of response categories), and the software has not been throughly tested. This software is distributed under a BSD license.

Executable versions of two programs for Windows 95/NT are available that compute a scale transformation for the multiple-choice and nominal response models, respectively. Use of these programs is discussed in the next section, as well as a link to download the programs. Following that, the source code for the programs discussed and a link to download the source code is given.

Executable Programs for Windows 95/NT

There are two executable Windows 95/NT programs - one for each model:

  1. mceq.exe - Equating for the muliple-choice model.
  2. nreq.exe - Equating for the nominal response model.

These are command-line programs that must be run from within a MS-DOS prompt window. To run a program type the program name followed by the name of a control file. For example, to run the example multiple-choice model equating provided with the programs type

    mceq mcm.in
where mcm.in is the control file for the example.

For both programs the control file should have five lines containing the following information:

  1. The name of a file containing item parameter estimates that are on the target scale (old form item parameter estimates).
  2. The name of a file containing item parameter estimates that are on the current scale (new form item parameter estimates).
  3. The name of a file containing theta points at which the objective function to be minimized in computing the scale transformation is evaluated.
  4. Name of a file where the program output will be written.
  5. A starting value for the intercept and slope, respectively, separated by one or more spaces.

The first line of the parameter files (first two files in the list above) should contain two integers separated by one or more spaces. The first integer should be the number of items used in the equating (number of items in common between the two forms being equated). The second number should be the total number of parameters to be read for each item. If R is the number of response categories then the number of parameters read should be 2*R for the nominal response model and 2*(R+1)+R for the multiple-choice model. The current version of the program requires that each item have the same number of response categories, and therefore the same number of parameters. Item parameters for each item are given on the second and following lines of the parameter files, one item per line. For the multiple-choice model the the first R+1 parameters read for each item should be the a-parameters, the second R+1 parameters should be the b-parameters, and the last R parameters should be the d-parameters (using the parameter notation in Kim and Hanson (2000)). The first a-parameter and the first b-parameter should be those corresponding to the guessing probabilities. Subsequent a- and b-parameters should be those associated with response categories. For example, the second a-parameter and second b-parameter should correspond to the first response category, along with the first d-parameter. For the nominal response model the first R parameters read for each item are the a-parameters, and the second R parameters are the b-parameters.

The first line of the theta file should contain the number of theta points to be used. The second and subsequent lines of the theta file should contain the theta values to be used, one per line.

The output file consists of output from the Uncmin++ minimization class which is used to minimize the negative of the objective function (which maximizes the objective function). The final values of the slope and intercept are given below the two lines that begin with 'OPTSTP'. The two lines begining with 'OPTSTP' indicate the status of the minimization routine at the last iteration. The slope and intercept of the scale transformation are the two numbers below the line containing 'Current x'. Do not confuse this line with the one earlier in the output which gives the starting values.

Included with the programs are example program input files used to compute the results for the example presented in Kim and Hanson (2000). The command file for the multiple-choice program is mcm.in, and the command file for the nominal response program is nrm.in. The output files corresponding to these command files are are mcm.out and nrm.out.

Download - Zip archive (188 KB) containing this HTML file along with two directories 'mcm' and 'nrm' containing the programs and examples for the multiple-choice model and nominal response model, respectively. All the text files contain DOS line breaks (they are DOS text files).

Source Code

Source code for the programs described above is separately available. The makefile used to compile these programs using the free Borland 5.5 compiler for Windows 95/NT is included. The makefile includes separate targets for the two programs. Also included is a makefile for compiling the programs using gcc on Linux.

The following files are included in the source code distribution:

Compiling the programs requires some other C++ source code I have make available:

These two packages will need to be downloaded and installed in order to compile the programs.

Download - Zip archive (12 KB) containing this HTML file along with the source files indicated above. These files all use DOS line endings (they are DOS text files).

Software by Brad Hanson

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URL of this page: http://www.b-a-h.com/software/mcmequate/index.html

Last updated: April 12, 2000

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