The Ability for Posterior Predictive Checking to Identify Model Misspecification in Bayesian Growth Mixture Modeling

Proper model specification is an issue for researchers, regardless of the estimation framework being utilized. Typically, indexes are used to compare the fit of one model to the fit of an alternate model. These indexes only provide an indication of relative fit and do not necessarily point toward proper model specification. There is a procedure in the Bayesian framework called posterior predictive checking that is designed theoretically to detect model misspecification for observed data. However, the performance of the posterior predictive check procedure has thus far not been directly examined under different conditions of mixture model misspecification. This article addresses this task and aims to provide additional insight into whether or not posterior predictive checks can detect model misspecification within the context of Bayesian growth mixture modeling. Results indicate that this procedure can only identify mixture model misspecification under very extreme cases of misspecification.