A Standardized Generalized Dimensionality Discrepancy Measure and a Standardized Model-Based Covariance for Dimensionality Assessment for Multidimensional Models

The standardized generalized dimensionality discrepancy measure and the standardized model-based covariance are introduced as tools to critique dimensionality assumptions in multidimensional item response models. These tools are grounded in a covariance theory perspective and associated connections between dimensionality and local independence. Relative to their precursors, they allow for dimensionality assessment in a more readily interpretable metric of correlations. A simulation study demonstrates the utility of the discrepancy measures' application at multiple levels of dimensionality analysis, and compares them to factor analytic and item response theoretic approaches. An example illustrates their use in practice.