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Loglinear Multidimensional IRT Models for Polytomously Scored Items

Published online by Cambridge University Press:  01 January 2025

Henk Kelderman  and
Carl P. M. Rijkes
Henk Kelderman*
Affiliation:
University of Twente
Carl P. M. Rijkes
Affiliation:
University of Twente
*
Requests for reprints should be sent to H. Kelderman, Department of Work and Organizational Psychology, Faculty of Psychology and Pedagogics, Vrije Universiteit, De Boelelaan 1081c, NL 1081 HV Amsterdam, THE NETHERLANDS.
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Abstract

A loglinear IRT model is proposed that relates polytomously scored item responses to a multidimensional latent space. The analyst may specify a response function for each response, indicating which latent abilities are necessary to arrive at that response. Each item may have a different number of response categories, so that free response items are more easily analyzed. Conditional maximum likelihood estimates are derived and the models may be tested generally or against alternative loglinear IRT models.

Keywords

multidimensional item response theoryloglinear modelRasch modelmultidimensional Rasch modelpolytomous responsespartial credit modelgoodness-of-fit testing
Type
Original Paper
Information
Psychometrika , Volume 59 , Issue 2 , June 1994 , pp. 149 - 176
Copyright
Copyright © 1994 The Psychometric Society

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Footnotes

1

Hank Kelderman is currently affiliated with Vrije Universiteit, Amsterdam.

We thank Linda Vodegel-Matzen of the Division of Developmental Psychology of the University of Amsterdam for making available the data used in the example in this article.

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