Hierarchical Bayes Modeling of Survey-weighted Small Area Proportions

When a Hierarchical Bayes area level model is used to produce estimates of proportions of units with a given characteristic for small areas, it is commonly assumed that the survey weighted proportion for each sampled small area has a normal distribution and that the sampling variance of this proportion is known. However, these assumptions are problematic when the small area sample size is small or when the true proportion is near 0 or 1. In an effort to overcome these problems, we test two alternative models for the survey weighted proportion using a Monte Carlo simulation study in which stratified simple random samples are generated from a fixed finite population. We compare the results obtained from these alternative models with those obtained from two commonly used models.