Hierarchical Bayesian Models for Noisy Size Responses from Small Areas

• Activity Number: 613 - Practical Applications of Small Area Estimation
• Type: Topic Contributed
• Date/Time: Thursday, August 3, 2017 : 8:30 AM to 10:20 AM
• Sponsor: Survey Research Methods Section
• Author(s): Binod Manandhar*
• Companies: Worcester Polytechnic Institute
• Keywords: GB2 distribution ; Generalized gamma distribution ; Logarithmic transformation ; Markov chain Monte Carlo ; Skewed distribution

Abstract

We implement the techniques of small area estimation (SAE) to study a positively skewed welfare indicator, consumption. A logarithmic transformation that may be problematic is usually suggested for positively skewed data to build a model. In our study, we have developed hierarchical Bayesian models without log-transformation. We applied our model to the Nepal Living Standards Survey, 2003/04 consumption data, an aggregate of all food and nonfood items consumed in the past twelve months. Since, the respondent has to recall the consumptions in the past twelve months, we assume that data are recorded with noises. For the noisy data, we fit three special cases of generalized beta distribution of the second kind (GB2) models using the Metropolis Hastings sampler. After fitting Bayesian models for SAE, we show how to select the most plausible model and perform the Bayesian data analysis.