6. Spatially Structured Random Effects: A Comparison of Three Popular Specifications

Random effects models are increasing in popularity (see, for example, Demidenko, 2004), partially because they have become estimable. One common specification is for the intercept term to be cast as a random effects, resulting in it representing variability about the conventional single-value, constant mean. The role of a random effects in this context may be twofold: (1) supporting inferences beyond the specific fixed values of covariates employed in an analysis; and, (2) accounting for correlation in a non-random sample of data being analyzed. Including a random effects term moves a frequentist analysis a bit closer to a Bayesian analysis, given that, for instance, the intercept term becomes a random variable rather than being a constant, and has a prior probability distribution (usually normal) attached to it. Nevertheless, a bone fide Bayesian analysis would have a random variable for each of the n intercept term components comprising such a random effects, maintaining some degree of differentiation here between the frequentist and Bayesian approaches.