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

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.