Posterior Predictive Model Checking for Multidimensionality in Item Response Theory

Roy Levy, Robert J. Mislevy, Sandip Sinharay

Research output: Contribution to journalArticlepeer-review

66 Scopus citations


If data exhibit multidimensionality, key conditional independence assumptions of unidimensional models do not hold. The current work pursues posterior predictive model checking, a flexible family of model-checking procedures, as a tool for criticizing models due to unaccounted for dimensions in the context of item response theory. Factors hypothesized to influence dimensionality and dimensionality assessment are couched in conditional covariance theory and conveyed via geometric representations of multidimensionality. A simulation study investigates the performance of the model-checking tools for dichotomous observables. Key findings include support for the hypothesized effects of the manipulated factors with regard to their influence on dimensionality assessment and the superiority of certain discrepancy measures for conducting posterior predictive model checking for dimensionality assessment.

Original languageEnglish (US)
Pages (from-to)519-537
Number of pages19
JournalApplied Psychological Measurement
Issue number7
StatePublished - Oct 1 2009


  • Conditional covariance theory
  • Item response theory
  • Local independence
  • Multidimensionality
  • Posterior predictive model checking

ASJC Scopus subject areas

  • Social Sciences (miscellaneous)
  • Psychology (miscellaneous)


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