Random effect modelling using Bayesian methods

Bayesian methods are increasingly used in a variety of academic disciplines, and important applications in ecology, medicine, management science, operations research and finance. The continued use of these methods depends on understanding the strengths and weaknesses of current Bayesian modelling practice. In this paper, we examine important implementation issues within the context of data analysis with statistical models which contain random effects or unmeasured heterogeneity. Random effect models provide an effective way to incorporate sources of variation not able to be modelled by covariate information, and these models lead naturally to Bayesian formulations using prior distributions for the variance components. We examine implications for specifying scale parameters in hierarchical models.