BAYESIAN PREDICTIVE INFERENCE FOR UNITS WITH SMALL SAMPLE SIZES - THECASE OF BINARY RANDOM-VARIABLES

The National Health Interview Survey is designed to produce precise es timates for the entire United States but not for individual states. In this study, Bayesian predictive inference is used to provide point es timates and measures of variability for the desired finite population quantities. The investigation reported here concerns binary random var iables such as the occurrence of at least one doctor visit within the past 12 months. The specification is hierarchic. First, for each clust er, there is a separate logistic regression relating a patient's proba bility of a doctor visit with his or her characteristics. Second, ther e is a multivariate linear regression linking the (cluster) regression parameters to covariates measured at the cluster level. A fully Bayes ian analysis is carried out; this technique provides gains over synthe tic estimation and conventional randomization-based analysis. The repo rted approach is potentially useful for any situation when the sample size associated with a unit of interest (e.g., a hospital or small geo graphic area) is too small to permit satisfactory inference using only the data from that unit.