Small Area Inference for Binary Variables in the National Health Interview Survey
针对国家健康访谈调查无法精确估计小区域或子群体的问题，提出贝叶斯分层模型，结合逻辑回归和多元线性回归，估计医生就诊概率等二元变量，并通过交叉验证和1990年人口普查数据验证方法准确性。
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 standard methods, that is, synthetic estimates and estimates obtained from a conventional randomization-based approach. We use a cross-validation exercise to assess the quality of model fit. We also summarize the results of a separate study of the binary indicator of partial work limitation. Because we know the value of this variable for each respondent to the 1990 Census long form, we can compare estimates corresponding to alternative methods and models with very accurate estimates of the true values. Key Words: Bayesian predictive inferenceCluster samplingCross-validationEmpirical BayesHierarchical modelLogistic regressionSynthetic estimates