A generalized dimensionality discrepancy measure for dimensionality assessment in multidimensional item response theory


Correspondence should be addressed to Dr Roy Levy, Arizona State University, PO Box 873701, Tempe, AZ 85287-3701, USA (e-mail: roy.levy@asu.edu).


A generalized dimensionality discrepancy measure is introduced to facilitate a critique of dimensionality assumptions in multidimensional item response models. Connections between dimensionality and local independence motivate the development of the discrepancy measure from a conditional covariance theory perspective. A simulation study and a real-data analysis demonstrate the utility of the discrepancy measure's application at multiple levels of analysis in a posterior predictive model checking framework.