339 – Official Statistics and Small Area Estimation
Bayesian Analysis of Multinomial Counts from Small Areas and Sub-Areas
Balgobin Nandram
Worcester Polytechnic Institute, Worcester, Massachusetts
Lu Chen
Worcester Polytechnic Institute, Worcester, Massachusetts
Binod Manandhar
University of Houston
A standard problem in official statistics is to predict the finite population proportion of a small area when individual-level data are available from a survey and more extensive data (covariates but not responses) are available from a census. The 2003-2004 Nepal Living Standards Survey and the 2001 census, that must be matched, provide an example. In the largest stratum less than one percent of the wards and 12 households within each sampled ward are sampled. Interest is on the health portion of the survey in which each individual in a household is categorized into one of four health classes. Using a two-stage procedure, we study the counts in the households within the wards and a projection method to infer about the nonsampled households and wards. This is accommodated by a four-stage hierarchical Bayesian model for multinomial counts. An output regression analysis is performed on the cell proportions, a projection method provides the nonsampled household counts, and posterior inference is made of the finite population proportions (FPPs). We compare two Bayesian models (area and sub-area) and two projection methods (parametric and nonparametric) via inference about the FPPs.