A note on posterior predictive checks to assess model fit for incomplete data.

We examine two posterior predictive distribution based approaches to assess model fit for incomplete longitudinal data. The first approach assesses fit based on replicated complete data as advocated in Gelman et al. (2005). The second approach assesses fit based on replicated observed data. Differences between the two approaches are discussed and an analytic example is presented for illustration and understanding. Both checks are applied to data from a longitudinal clinical trial. The proposed checks can easily be implemented in standard software like (Win)BUGS/JAGS/Stan.