Empirical Bayes and Bayes hierarchical models have been used extensively for small area estimation. However, the sampling weights that are required to reflect complex surveys are rarely considered in these models. In this paper, we develop a method to incorporate the sampling weights for binary data when estimating, for example, small area proportions or predicting small area counts. We consider empirical Bayes beta-binomial models, and normal hierarchical models. The latter may include spatial random effects, with computation carried out using the integrated nested Laplace approximation, which is fast. A simulation study is presented, to demonstrate the performance of the proposed approaches, and to compare results from models with and without the sampling weights. The results show that estimation mean squared error can be greatly reduced using the proposed models, when compared with more standard approaches. Bias reduction occurs through the incorporation of sampling weights, with variance reduction being achieved through hierarchical smoothing. We also analyze data taken from the Washington 2006 Behavioral Risk Factor Surveillance System.
keywords:Integrated Nested Laplace Approximations; Poststratification; Sample Surveys; Spatial Smoothing.