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Exact Person Fit Indexes for the Rasch Model for Arbitrary Alternatives

Published online by Cambridge University Press:  02 January 2025

Ivo Poncny
Ivo Poncny*
Affiliation:
University of Vienna
*
Requests for reprints should be sent to Ivo Ponocny, Institut für Psychologie, Universität Wien, Liebiggasse 5, A-1010 Wien, AUSTRIA. E-mail: ivo.ponocny@univie.ac.at.
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Abstract

A new algorithm for obtaining exact person fit indexes for the Rasch model is introduced which realizes most powerful tests for a very general family of alternative hypotheses, including tests concerning DIF as well as model-deviating item correlations. The method is also used as a goodness-of-fit test for whole data sets where the item parameters are assumed to be known. For tests with 30 items at most, exact values are obtained, for longer tests a Monte Carlo-algorithm is proposed. Simulated examples and an empirical investigation demonstrate test power and applicability to item elimination.

Keywords

DIFexact testsIRTperson fitRasch model
Type
Original Paper
Information
Psychometrika , Volume 65 , Issue 1 , March 2000 , pp. 29 - 42
Copyright
Copyright © 2000 The Psychometric Society

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Footnotes

The author wishes to thank Elisabeth Ponocny-Seliger and the reviewers for many helpful comments. All exact goodness-of-fit tests proposed in this article are implemented in the menu-driven program T-Rasch 1.0 by Ponocny and Ponocny-Seliger (1999) which can be obtained from ProGAMMA (WWW: http://www.gamma.rug.nl) and also performs nonparametric tests.

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