This article proposes methodology for assessing goodness of fit in Bayesian hierarchical models. The methodology is based on comparisons of the posterior distributions of pivotal discrepancy measures to known reference distributions at various levels of model hierarchies. Because resulting diagnostics can be calculated from the standard output of Markov chain Monte Carlo algorithms, their computational costs are minimal. Several simulation studies are provided, each of which suggests that diagnostics based on pivotal discrepancy measures have higher statistical power than comparable posterior-predictive diagnostic checks in detecting model departures. The proposed methodology is illustrated in a clinical applications.
Johnson, Valen, "Goodness-of-fit Diagnostics for Bayesian Hierarchical Models" (December 2010). UT MD Anderson Cancer Center Department of Biostatistics Working Paper Series. Working Paper 69.