Goodness-of-Fit Diagnostics for Bayesian Hierarchical Models
Version of Record online: 3 NOV 2011
© 2011, The International Biometric Society
Volume 68, Issue 1, pages 156–164, March 2012
How to Cite
Yuan, Y. and Johnson, V. E. (2012), Goodness-of-Fit Diagnostics for Bayesian Hierarchical Models. Biometrics, 68: 156–164. doi: 10.1111/j.1541-0420.2011.01668.x
- Issue online: 23 MAR 2012
- Version of Record online: 3 NOV 2011
- Received September 2010. Revised June 2011. Accepted July 2011.
- Discrepancy measures;
- Markov chain Monte Carlo;
- Model checking;
- Model criticism;
- Model hierarchy;
- Posterior-predictive density
Summary This article proposes methodology for assessing goodness of fit in Bayesian hierarchical models. The methodology is based on comparing values of pivotal discrepancy measures (PDMs), computed using parameter values drawn from the posterior distribution, to known reference distributions. Because the resulting diagnostics can be calculated from 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 PDMs have higher statistical power than comparable posterior-predictive diagnostic checks in detecting model departures. The proposed methodology is illustrated in a clinical application; an application to discrete data is described in supplementary material.