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Paradoxical Results and Item Bundles

Published online by Cambridge University Press:  01 January 2025

Giles Hooker  and
Matthew Finkelman
Giles Hooker*
Affiliation:
Cornell University
Matthew Finkelman
Affiliation:
Tufts School of Dental Medicine
*
Requests for reprints should be sent to Giles Hooker, Cornell University, Ithaca, NY, USA. E-mail: giles.hooker@cornell.edu
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Abstract

Hooker, Finkelman, and Schwartzman (Psychometrika, 2009, in press) defined a paradoxical result as the attainment of a higher test score by changing answers from correct to incorrect and demonstrated that such results are unavoidable for maximum likelihood estimates in multidimensional item response theory. The potential for these results to occur leads to the undesirable possibility of a subject’s best answer being detrimental to them. This paper considers the existence of paradoxical results in tests composed of item bundles when compensatory models are used. We demonstrate that paradoxical results can occur when bundle effects are modeled as nuisance parameters for each subject. However, when these nuisance parameters are modeled as random effects, or used in a Bayesian analysis, it is possible to design tests comprised of many short bundles that avoid paradoxical results and we provide an algorithm for doing so. We also examine alternative models for handling dependence between item bundles and show that using fixed dependency effects is always guaranteed to avoid paradoxical results.

Keywords

item response theorymultidimensional item response theorylikelihoodparadoxical resultsitem bundlerandom effectsfixed dependency effects
Type
Theory and Methods
Information
Psychometrika , Volume 75 , Issue 2 , June 2010 , pp. 249 - 271
Copyright
Copyright © 2010 The Psychometric Society

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Footnotes

The authors would like to thank an anonymous referee of Hooker et al. (2009) for suggesting the problem of item bundles.

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