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Nonparametric Goodness-of-Fit Tests for the Rasch Model

Published online by Cambridge University Press:  01 January 2025

Ivo Ponocny
Ivo Ponocny*
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 Monte Carlo algorithm realizing a family of nonparametric tests for the Rasch model is introduced which are conditional on the item and subject marginals. The algorithm is based on random changes of elements of data matrices without changing the marginals; most powerful tests against all alternative hypotheses are given for which a monotone characteristic may be computed from the data matrix; alternatives may also be composed. Computation times are long, but exactp-values are approximated with the quality of approximation only depending on calculation time, but not on the number of persons. The power and the flexibility of the procedure is demonstrated by means of an empirical example where, among others, indicators for increased item similarities, the existence of subscales, violations of sufficiency of the raw score as well as learning processes were found. Many of the features described are implemented in the program T-Rasch 1.0 by Ponocny and Ponocny-Seliger (1999).

Keywords

nonparametric testsIRTgoodness-of-fit testsRasch modelexact tests
Type
Articles
Information
Psychometrika , Volume 66 , Issue 3 , September 2001 , pp. 437 - 459
Copyright
Copyright © 2001 The Psychometric Society

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Footnotes

The author wishes to thank Alexander Kaba, Birgit Bukasa, and Ulrike Wenninger of Österreichisches Kuratorium für Verkehrssicherheit (Austrian Traffic Safety Board) for allowing a data set to be used for the empirical example, and Elisabeth Ponocny-Seliger and the reviewers for many helpful comments. The menu-driven program T-Rasch 1.0 by Ponocny and Ponocny-Seliger (1999) can be obtained from Assessment Systems Corporation (http: //www.assess.com) or from the authors. (Note that it also performs exact person fit tests.)

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