ABSTRACT

Traditional treatment of random effects in mixed linear and nonlinear models generally assumes that these effects are independent following some standard distributions such as normal or gamma. However, with the advent of Markov chain Monte Carlo (MCMC) methods and, in particular, the Gibbs sampler (cf. Gelfand and Smith, 1990), such restrictions are no longer necessary, and a much broader class of models, including those with correlated random effects, can be used in practice. (See Clayton (1996) for a general review of this recent development.)

In this chapter we consider generalized mixed linear models with random effects having the autoregressive and conditionally autoregressive properties commonly encountered in temporal and spatial covariates where one expects similarities among closely situated observations. Examples from disease mapping will be used to motivate these models.