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Generalizations of Paradoxical Results in Multidimensional Item Response Theory

Published online by Cambridge University Press:  01 January 2025

Pascal Jordan  and
Martin Spiess
Pascal Jordan*
Affiliation:
University of Hamburg
Martin Spiess
Affiliation:
University of Hamburg
*
Requests for reprints should be sent to Pascal Jordan, University of Hamburg, Von-Melle-Park 5, 20146 Hamburg, Germany. E-mail: pascal.jordan@uni-hamburg.de
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Abstract

Maximum likelihood and Bayesian ability estimation in multidimensional item response models can lead to paradoxical results as proven by Hooker, Finkelman, and Schwartzman (Psychometrika 74(3): 419–442, 2009): Changing a correct response on one item into an incorrect response may produce a higher ability estimate in one dimension. Furthermore, the conditions under which this paradox arises are very general, and may in fact be fulfilled by many of the multidimensional scales currently in use. This paper tries to emphasize and extend the generality of the results of Hooker et al. by (1) considering the paradox in a generalized class of IRT models, (2) giving a weaker sufficient condition for the occurrence of the paradox with relations to an important concept of statistical association, and by (3) providing some additional specific results for linearly compensatory models with special emphasis on the factor analysis model.

Keywords

multidimensional item response theoryparadoxical resultsreverse rule functionsmultidimensional graded response modelsimple structurefactor analysis

Information

Type
Article
Information
Psychometrika , Volume 77 , Issue 1 , January 2012 , pp. 127 - 152
Copyright
Copyright © 2011 The Psychometric Society

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