Bayesian Estimation in Small Areas Under Prestratification and Poststratification

• Activity Number: 115
• Type: Topic Contributed
• Date/Time: Monday, August 4, 2003 : 10:30 AM to 12:20 PM
• Sponsor: Section on Bayesian Stat. Sciences
• Author(s): Jacob J. Oleson*+ and Zhuoqiong (Chong) He and Dongchu Sun
• Companies: Arizona State University and University of Missouri, Columbia and University of Missouri, Columbia
• Keywords: stratification ; MCMC ; Bayesian prediction ; random sample size ; spatial correlation

Abstract

The purpose of this work is to incorporate both pre- and post-stratification into a Bayesian hierarchical framework. A generalized linear model with possible correlated random effects is often used when there is one unknown parameter. We propose a new family of generalized linear mixed models with correlated random effects when there are two unknown canonical parameters. This is the case when the sample size is considered random. Current methods for handling cases of this nature are not suitable. Such a family can be used to model both random sample sizes and success probabilities in small area estimation under pre- and post-stratification. General formulae for Bayesian estimation and prediction at the post-stratification level are given. One application is the 1998 Missouri Turkey Hunting Survey, which was prestratified based on the hunters place of residence. Success rates, hunting pressure, and harvests are of interest at the poststratified county level. Results show that there are significant spatial correlations between counties and the variability at the poststratification level is reduced with the prestratification.