Small Area Inference for Binary Variables in the National Health Interview Survey

Abstract The National Health Interview Survey is designed to produce precise estimates of finite population parameters for the entire United States but not for small geographical areas or subpopulations. Our investigation concerns estimates of proportions such as the probability of at least one visit to a doctor within the past 12 months. To include all sources of variation in the model, we carry out a Bayesian hierarchical analysis for the desired finite population quantities. First, for each cluster (county) a separate logistic regression relates the individual's probability of a doctor visit to his or her characteristics. Second, a multivariate linear regression links cluster regression parameters to covariates measured at the cluster level. We describe the numerical methods needed to obtain the desired posterior moments. Then we compare estimates produced using the exact numerical method with approximations. Finally, we compare the hierarchical Bayes estimates to empirical Bayes estimates and to stand...