A Bayesian Approach to Small Area Estimation of Health Insurance Coverage

Small area estimation focuses on borrowing strength across area in order to develop a reliable estimator when the auxiliary information is available. The traditional methods for small area estimation borrow strength through linear models that provide links to related areas, which may not be appropriate for some survey data. We examine the empirical best unbiased linear prediction method and hierarchical Bayes method with the Louisiana Health Insurance Survey (LHIS), and a hierarchical Bayes method with probit model to fit the LHIS data by using the single year data in 2013. This approach results in a lower level of posterior standard deviations compared to the other two estimates. Furthermore, we also construct an informative Bayesian prior on the repeated cross-sectional data set 2003-2013, and show a continuous shift from the single year estimates to the pooled estimates. Simulation studies are given to examine the performance of various approaches.