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Posterior Predictive Model Checking for Conjunctive Multidimensionality in Item Response Theory

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  • Roy Levy

Abstract

If data exhibit multidimensionality, key conditional independence assumptions of unidimensional models do not hold. The current work pursues posterior predictive model checking (PPMC) as a tool for criticizing models due to unaccounted for dimensions in data structures that follow conjunctive multidimensional models. These pursuits are couched in previous work investigating factors influencing dimensionality and dimensionality assessment. A simulation study investigates the model checking tools in the context of item response theory (IRT) for dichotomous observables, in which a unidimensional model is fit to data that follow a conjunctive multidimensional model. Key findings include (a) support for the hypothesized effects of the manipulated factors and (b) the superiority of certain discrepancy measures for conducting PPMC for dimensionality assessment.

Suggested Citation

  • Roy Levy, 2011. "Posterior Predictive Model Checking for Conjunctive Multidimensionality in Item Response Theory," Journal of Educational and Behavioral Statistics, , vol. 36(5), pages 672-694, October.
    • Handle: RePEc:sae:jedbes:v:36:y:2011:i:5:p:672-694
    DOI: 10.3102/1076998611410213
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    References listed on IDEAS

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    1. Eric Bradlow & Howard Wainer & Xiaohui Wang, 1999. "A Bayesian random effects model for testlets," Psychometrika, Springer;The Psychometric Society, vol. 64(2), pages 153-168, June.
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    3. Jinming Zhang & William Stout, 1999. "Conditional covariance structure of generalized compensatory multidimensional items," Psychometrika, Springer;The Psychometric Society, vol. 64(2), pages 129-152, June.
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