Bayesian Posterior Predictive Checks for Complex Models

In sociological research, it is often difficult to compare nonnested models and to evaluate the fit of models in which outcome variables are not normally distributed. In this article, the authors demonstrate the utility of Bayesian posterior predictive distributions specifically, as well as a Bayesian approach to modeling more generally, in tackling these issues. First, they review the Bayesian approach to statistics and computation. Second, they discuss the evaluation of model fit in a bivariate probit model. Third, they discuss comparing fixed- and random-effects hierarchical linear models. Both examples highlight the use of Bayesian posterior predictive distributions beyond these particular cases.