Hierarchical Bayes small area estimation under a spatial model with application to health survey data - ARCHIVED

In this paper we study small area estimation using area level models. We first consider the Fay-Herriot model (Fay and Herriot 1979) for the case of smoothed known sampling variances and the You-Chapman model (You and Chapman 2006) for the case of sampling variance modeling. Then we consider hierarchical Bayes (HB) spatial models that extend the Fay-Herriot and You-Chapman models by capturing both the geographically unstructured heterogeneity and spatial correlation effects among areas for local smoothing. The proposed models are implemented using the Gibbs sampling method for fully Bayesian inference. We apply the proposed models to the analysis of health survey data and make comparisons among the HB model-based estimates and direct design-based estimates. Our results have shown that the HB model-based estimates perform much better than the direct estimates. In addition, the proposed area level spatial models achieve smaller CVs than the Fay-Herriot and You-Chapman models, particularly for the areas with three or more neighbouring areas. Bayesian model comparison and model fit analysis are also presented.