ABSTRACT
This chapter is concerned with the application of hierarchical prior schemes to regressions involving univariate responses, where the observations are non-nested, but may be spatially or temporally configured. It illustrates of regression modelling invoking hierarchical principles, much attention has focused on Bayesian methods for predictor selection, commonly using selection indicators or shrinkage priors. The chapter considers many regression selection applications involve categorical predictors, including analysis of variance, and the particular issues. It explores hierarchical specfications also apply when latent responses or random effects are used to improve data representation in overdispersed general linear models and explains generate latent continuous responses underlying discrete observations. The chapter also considers heterogeneity in regression relationships or variance parameters over exchangeable sample units. Binomial regression with excess variation may occur when responses are arranged in clusters and responses from the same cluster are correlated: examples occur in teratological studies.
