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Posterior Predictive Model Checking for Multidimensionality in Item Response TheoryArizona State University, Roy.Levy{at}asu.edu
University of Maryland
Educational Testing Service 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.
Key Words: posterior predictive model checking • multidimensionality • local independence • item response theory • conditional covariance theory
This version was published on October
1, 2009 Applied Psychological Measurement, Vol. 33, No. 7,
519-537 (2009) |
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