, Volume 74, Issue 3, pp 419–442

Paradoxical Results in Multidimensional Item Response Theory

  • Giles Hooker
  • Matthew Finkelman
  • Armin Schwartzman
Theory and Methods

DOI: 10.1007/s11336-009-9111-6

Cite this article as:
Hooker, G., Finkelman, M. & Schwartzman, A. Psychometrika (2009) 74: 419. doi:10.1007/s11336-009-9111-6


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.


item response theory multidimensional item response theory likelihood monotonicity paradoxical results stochastic order maximum likelihood estimate a posteriori estimate 

Copyright information

© The Psychometric Society 2009

Authors and Affiliations

  • Giles Hooker
    • 1
  • Matthew Finkelman
    • 2
  • Armin Schwartzman
    • 3
  1. 1.Cornell UniversityIthacaUSA
  2. 2.Tufts University School of Dental MedicineBostonUSA
  3. 3.Harvard School of Public HealthBostonUSA

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