# Item Response Theory/Rasch models in SPSS Statistics

## Technote (troubleshooting)

## Problem(Abstract)

I have data that represents responses to a set of test questions (or attitude survey items), with 1 variable for each question. It has been suggested that I should analyze these variables with an Item Response Theory (IRT) model. Please provide a brief definition of IRT models. Does SPSS include procedures for IRT analysis? Can Rasch models be tested with SPSS?

## Resolving the problem

The basic idea of IRT models (also known as latent trait models) is that there is an underlying trait - a skill or knowledge level or an attitude, for example, that is reflected in the response to the test or survey items. The probability of getting each item correct (or agreeing to it, in an attitude survey) is a function of the item's difficulty and the 'amount' of the underlying trait in the respondent. In building the test, you hope to find items with difficulty levels across the range of ability in your target population of testees. In 2-parameter models, the slope of the IRT function (discrimination) is the second parameter to estimate. 3-parameter models include a 'guessing' parameter, usually for multiple-choice items. Rasch models are 1-parameter models, but they are also based on a different philosophy of test analysis and construction than higher-parameter IRT models. For a chart that provides distinctions and similarities between the Rasch and 1-Parameter Logistic (1-PL) IRT model, see the following online article.

Linacre J.M. (2005). Rasch dichotomous model vs. One-parameter Logistic Model. Rasch Measurement Transactions, 19:3, 1032.

http://www.rasch.org/rmt/rmt193h.htm

SPSS does not have any built-in procedures for IRT models. As of this writing, much IRT research is still conducted with specialized IRT software, such as that produced by Scientific Software, Assessment Systems Corp. and Winsteps (for Rasch models), for example. An enhancement request has been filed with SPSS Development. However, the SPSS Community at IBM developerWorks provides a set of Extension commands that can be installed into the SPSS Statistics directory to extend the capabilities of the program. These extension commands require the programmability plug-ins for R and/or Python. There are IRT-based extension commands available for SPSS versions 17 and above for users that have installed the SPSS Programmability module and the R plugins. Click the "Download materials for IBM SPSS Statistics" link in the SPSS Community site to learn more about the programmability plug-ins and the extension commands.

As of this writing, there are four extension commands that apply IRT-based analyses. The commands and descriptions from the extensions page are:

1. SPSSINC RASCH - downloaded from the SPSSINC_RASCH.zip link in the extensions page.

R Extension Command for Rasch Models

Version: 1.1.0, Minimum Statistics Version: 17.0.0, Author: AR, IBM SPSS

As of Statistics Version 19, this package is included in the R Essentials.

This package provides a procedure and a dialog box interface for estimation of Rasch models.

It requires R, the R Plug-Ins and the R package ltm.

2, STATS EXRASCH - downloaded from the STATS_EXRASCH.spe link in the extensions page.

It requires R, the R Plug-Ins and the R package eRm.

Minimum Statistics Version: 18

This procedure calculates standard Rasch models and five extensions: RM: Binary Rasch, 0/1 item values; LLTM: Linear Logistic Test, 0/1 item values; RSM: Polytomous Rating Scale, more than two values; LRSM: Linear Rating Scale, more than two values; PCM: Polytomous Partial Credit, more than two values; LPCM: Polytomous Linear Partial Credit, more than two values

3. STATS IRM - downloaded from the STATS_IRM.spe link in the extensions page.

The STATS IRM command fits three-parameter logistic (3-PL) item response models using the tpm function from the R ltm package. It is assumed that the values of the item variables are 0,1. By default, the procedure produces estimates of the model coefficients, and you can request optional output such as the item fit statistics, plots of the factor scores, and item characteristic curves, and save person-fit statistics to a new dataset. This extension command does not have options to constrain the discrimination parameter to equal a specified value or have a common estimated value or to fix the guessing parameter to 0. Therefore the one-parameter (1-PL) and two-parameter (2-PL) logistic IRT models are not currently available.

4. STATS GRM - downloaded from the STATS_GRM.spe link in the extensions page.

This package fits the Graded Response model for ordinal polytomous data via an IRT approach. It requires R, the R plugin, and the R package ltm.

All four of the above extension commands require at least version 17.0 of SPSS Statistics. The "Essentials and Plugins area of the "Downloads for IBM SPSS Statistics" page will help you install the programmability tools and the correct versions of Python and R for your version of SPSS Statistics. Once an extension command has been downloaded to your computer, it can be installed from the

Utilities->Extension Bundles->Install Local Extension Bundle in SPSS Statistics. As of SPSS Statistics v. 22, the download and installation steps can be performed in one step from the SPSS menu Utilities->Extension Bundles->Download and Install Extension Bundles. If installing from Windows 7 or 8, be sure that SPSS Statistics was launched in "Run as administrator" mode. (Right-click the SPSS Statistics icon on the desktop or Start menu and choose "Run as administrator".

Note that the R packages ltm and eRM, which are listed above, are installed when you install the respective extension commands.

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### Document information

**More support for:**
SPSS Statistics

**Software version:**
Not Applicable

**Operating system(s):**
Platform Independent

**Reference #:**
1488442

**Modified date:**
07 September 2016