A Comparison of the Rasch Model and Constrained Item Response Theory Models for Pertinent Psychological Test Data

Abstract

This paper provides an application of a generalization of the dichotomous Rasch model (RM) to the study of guessing behavior of respondents to typical achievement tests. One of the models applied is a constrained version of the 3PL model where a lower asymptote parameter is assumed in order to account for guessing behavior, but no variation of item discrimination is modeled. In addition, an application of mixture-distribution RMs aimed at modeling guessing effects and a comparison of the two approaches is presented. If such a constrained 3PL model is applied, in particular, to tests consisting of multiplechoice formatted items, the lower asymptote parameter can be interpreted as a guessing parameter. Therefore, the model is called the difficulty plus guessing PL (DGPL) model. An empirical example shows that a multiplechoice item pool only fits the Rasch model after a large number of items have been deleted, while the DGPL model can save most of those deleted items as it takes the severe but item-specific guessing effects into consideration. Furthermore, multiclass mixed RM analyses show — in comparison to the Rasch model — a good fit of the data and confirm item-specific guessing effects.