SMALL-AREA INFERENCE FOR BINARY VARIABLES IN THE NATIONAL-HEALTH-INTERVIEW-SURVEY

The National Health Interview Survey is designed to produce precise es timates of finite population parameters for the entire United Stares b ut not for small geographical areas or subpopulations. Our investigati on concerns estimates of proportions such as the probability of at lea st one visit to a doctor within the past 12 months. To include all sou rces of variation in the model, we carry out a Bayesian hierarchical a nalysis 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 numerica l methods needed to obtain the desired posterior moments. Then we comp are estimates produced using the exact numerical method with approxima tions. Finally, we compare the hierarchical Bayes estimates to empiric al Bayes estimates and to standard methods, that is, synthetic estimat es and estimates obtained from a conventional randomization-based appr oach. We use a cross-validation exercise to assess the quality of mode l fit. We also summarize the results of a separate study of the binary indicator of partial work limitation. Because we know the value of th is variable for each respondent to the 1990 Census long form, we can c ompare estimates corresponding to alternative methods and models with very accurate estimates of the true values.