Posterior predictive model checking for conjunctive multidimensionality in item response theory

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.