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Testing Unidimensionality in Polytomous Rasch Models

Published online by Cambridge University Press:  01 January 2025

Karl Bang Christensen ,
Jakob Bue Bjorner ,
Svend Kreiner  and
Jørgen Holm Petersen
Karl Bang Christensen*
Affiliation:
National Institute of Occupational Health, Denmark Department of Biostatistics, University of Copenhagen
Jakob Bue Bjorner
Affiliation:
National Institute of Occupational Health, Denmark
Svend Kreiner
Affiliation:
Department of Biostatistics, University of Copenhagen
Jørgen Holm Petersen
Affiliation:
Department of Biostatistics, University of Copenhagen
*
Requests for reprints should be sent to Karl Bang Christensen, National Institute of Occupational Health, Lersø Parkallé 105, 2100 KBH Ø, DENMARK. E-Mail: kbc@ami.dk
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Abstract

A fundamental assumption of most IRT models is that items measure the same unidimensional latent construct. For the polytomous Rasch model two ways of testing this assumption against specific multidimensional alternatives are discussed. One, a marginal approach assuming a multidimensional parametric latent variable distribution, and, two, a conditional approach with no distributional assumptions about the latent variable. The second approach generalizes the Martin-Löf test for the dichotomous Rasch model in two ways: to polytomous items and to a test against an alternative that may have more than two dimensions. A study on occupational health is used to motivate and illustrate the methods.

Keywords

polytomous Rasch modelunidimensionality assumptionMartin-Löf test
Type
Articles
Information
Psychometrika , Volume 67 , Issue 4 , December 2002 , pp. 563 - 574
Copyright
Copyright © 2002 The Psychometric Society

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Footnotes

The authors would like to thank Niels Keiding, Klaus Larsen and the anonymous reviewers for valuable comments to a previous version of this paper. This research was supported by a grant from the Danish Research Academy and by a general research grant from Quality Metric, Inc.

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