Bayesian model comparison and model averaging for small-area estimation

This paper considers small-area estimation with proportion data, and discusses the choice of upper-level model for the variation over areas. Inference about the random effects for the areas may depend strongly on the choice of this model, but this choice is not a straightforward matter. We show that posterior distributions of the deviances for the competing models provide a valuable tool for this purpose, and for the model averaging needed when several models fit equally well. We illustrate the approach with a well-known data set, and contrast it with the deviance information criterion approach.