Model Evaluation in the Presence of Categorical Data: Bayesian Model Checking as an Alternative to Traditional Methods.

Statistical analysis of categorical data often relies on multiway contingency tables; yet, as the number of categories and/or variables increases, the number of table cells with few (or zero) observations also increases. Unfortunately, sparse contingency tables invalidate the use of standard goodness-of-fit statistics. Limited-information fit statistics and bootstrapping procedures offer valuable solutions to this problem, but they present an additional concern in their strict reliance on the (potentially misleading) observed data. To address both of these issues, we demonstrate the Bayesian model checking technique, which yields insightful, useful, and comprehensive evaluations of specific properties of a given model. We illustrate this technique using item response data from a patient-reported psychopathology screening questionnaire, and we provide annotated R code to promote dissemination of this informative method in other prevention science modeling scenarios.