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

  • Klaus D. Kubinger
  • Clemens Draxler
Part of the Statistics for Social and Behavioral Sciences book series (SSBS)


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.


Model Check Item Parameter Marginal Likelihood Item Pool Person Parameter 
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Copyright information

© Springer Science + Business Media, LLC 2007

Authors and Affiliations

  • Klaus D. Kubinger
    • 1
  • Clemens Draxler
    • 2
  1. 1.Vienna UniversityWienAustria
  2. 2.Leibniz Institute for Science EducationKielGermany

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