Model Criticism of Growth Curve Models via Posterior Predictive Model Checking

Longitudinal data structures are frequently encountered in a variety of disciplines in the social and behavioral sciences. Growth curve modeling offers a highly extensible framework that allows for the exploration of rich hypotheses. However, owing to the presence of interrelated sources of potential data-model misfit at multiple levels, the matter of model criticism remains challenging for even foundational growth curve models. Through a simulation study and an applied example, the performance of six discrepancy measures was investigated using posterior predictive model checking as the framework for model criticism. The likelihood ratio and the standardized generalized dimensionality discrepancy measure outperformed the other discrepancy measures under consideration and show promise for future study and use.