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Paradoxical Results in Multidimensional Item Response Theory

Published online by Cambridge University Press:  01 January 2025

Giles Hooker ,
Matthew Finkelman  and
Armin Schwartzman
Giles Hooker*
Affiliation:
Cornell University
Matthew Finkelman
Affiliation:
Tufts University School of Dental Medicine
Armin Schwartzman
Affiliation:
Harvard School of Public Health
*
Requests for reprints should be sent to Giles Hooker, Cornell University, Ithaca, NY 14853, USA. E-mail: [email protected]
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Abstract

In multidimensional item response theory (MIRT), it is possible for the estimate of a subject’s ability in some dimension to decrease after they have answered a question correctly. This paper investigates how and when this type of paradoxical result can occur. We demonstrate that many response models and statistical estimates can produce paradoxical results and that in the popular class of linearly compensatory models, maximum likelihood estimates are guaranteed to do so. In light of these findings, the appropriateness of multidimensional item response methods for assigning scores in high-stakes testing is called into question.

Keywords

item response theorymultidimensional item response theorylikelihoodmonotonicityparadoxical resultsstochastic ordermaximum likelihood estimatea posteriori estimate
Type
Theory and Methods
Information
Psychometrika , Volume 74 , Issue 3 , September 2009 , pp. 419 - 442
Copyright
Copyright © 2009 The Psychometric Society

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