IRT-FIT: SAS® Macros for Fitting Item Response Theory (IRT) Models

Psychometrics has recently seen the development of complex measurement models to better represent test and item data. Item Response Theory (IRT), in particular, comprises a set of non-linear latent variable models that appear to have several conceptual and empirical properties that make them more valuable in practice than classical test theory methods. However, IRT-based models typically require the availability of costly and computationallyintensive software for estimating parameters and assessing model fit. In this paper, we present a set of SAS Macros called IRT-FIT, which use SAS /IML® and SAS/GRAPH® to estimate, fit, and graph twoand three-parameter IRT models to binary test data. The macros currently developed use Bock and Aitkin’s (1981) Marginal Maximum Likelihood (MML) estimation algorithm for fitting models and estimating parameters as the basis for the computations. Additionally, we have extended the MML routines by implementing Bayesian Estimation concepts as suggested in Mislevy (1986). All computational routines are written in SAS/IML, and output data sets are produced containing the parameter estimates along with their associated standard errors and overall model fit statistics. Optionally, SAS/GRAPH plots are available of the estimated Item Characteristic Curves (ICC’s), the item and test information curves, as well as the standard error curve for estimated latent trait scores. Finally, if the test data come from a rating experiment and a cut-point along the latent variable can be determined, ROC curves using IRT-based estimates of Signal-Detection-Theory concepts are plotted to visually represent rater performance.