Bayesian Predictive Inference Under Benchmarking of Body Mass Index and Bone Mineral Density for Small Domains

• Activity Number: 400
• Type: Topic Contributed
• Date/Time: Tuesday, August 2, 2011 : 2:00 PM to 3:50 PM
• Sponsor: Section on Bayesian Statistical Science
• Author(s): Ma Criselda Toto*+
• Companies: National Institute of Statistical Sciences
• Keywords: bayesian predictive inference ; multivariate ; small area estimation ; benchmarking

Abstract

In sample survey of finite populations, small domains are subpopulations for which the sample sizes are too small for estimation of adequate precision. Considering the population of Mexican American adults (20 years and above) from the large counties of New York, we implement Bayesian predictive inference to estimate the finite population means of body mass index (BMI) and bone mineral density (BMD) from the Third National Health and Nutrition Examination Survey (NHANES III). Generally, models used in small area estimation do not make use of the unit-level weights. We use a Bayesian nested-error regression model with internal benchmarking constraints that incorporate unit-level sampling weights. Benchmarking is done by applying constraints that will ensure that the `total' of the small domain estimates matches the `grand total'. Benchmarking can help prevent model failure, an important issue in small area estimation. It can also lead to improved prediction because of the information incorporated in the sample space due to the additional constraint. We present results for the multivariate benchmarking Bayesian model and compare the outcomes with its univariate counterpart.