Small-Area Estimation with Uncertain Random Effects

• Activity Number: 162
• Type: Topic Contributed
• Date/Time: Monday, July 30, 2012 : 10:30 AM to 12:20 PM
• Sponsor: Section on Survey Research Methods
• Author(s): Gauri Datta*+ and Abhyuday Mandal and Anthony Wanjoya
• Companies: University of Georgia and University of Georgia and University of Georgia
• Keywords: Fay-Herriot model ; Area level data ; empirical Bayes ; hierarchical Bayes

Abstract

Random effects models play important roles in model-based small area estimation. Random effects account for lack of fit of the regression of the population small area means on appropriate explanatory variables. It is possible that these covariates explain variation of some of small area means reasonably well, but not so well for the other areas. As a flexible alternative to random effects model, we propose a mixture model. For small areas whose population means are adequately explained by covariates, the model does not add any random model error, and for the other areas, a random component is added to the regression. This is a flexible alternative where the data determine the extent of lack of fit of the regression model for a particular small area, and add a random effect if needed. We use this mixture model to estimate poverty counts for US counties. With simulated data in SAIPE setup, we evaluate the small area estimates from the mixture model in terms of average absolute relative bias and squared relative bias. Measured in terms of these biases, our simulation study shows that the new estimates are more accurate than the estimates resulting from the standard Fay-Herriot model.