Bayesian spatial models for small area estimation of proportions

This article presents a logistic hierarchical model approach for small area prediction of proportions, taking into account both possible spatial and unstructured heterogeneity effects. The posterior distributions of the proportion predictors are obtained via Markov Chain Monte Carlo methods. This automatically takes into account the extra uncertainty associated with the hyperparameters. The procedures are applied to a real data set and comparisons are made under several settings, including a quite general logistic hierarchical model with spatial structure plus unstructured heterogeneity for small area effects. A model selection criterion based on the Expected Prediction Deviance is proposed. Its utility for selecting among competitive models in the small area prediction context is examined.