Flexible parametric models for random-effects distributions

Abstract

It is commonly assumed that random effects in hierarchical models follow a normal distribution. This can be extremely restrictive in practice. We explore the use of more flexible alternatives for this assumption, namely the τ distribution, and skew extensions to the normal and τ distributions, implemented using Markov Chain Monte Carlo methods. Models are compared in terms of parameter estimates, deviance information criteria, and predictive distributions. These methods are applied to examples in meta-analysis and health-professional variation, where the distribution of the random effects is of direct interest. The results highlight the importance of allowing for potential skewing and heavy ..