Multivariate Fay-Herriot Bayesian Estimation of Small Area Means Under Functional Measurement Error

• Activity Number: 567 - Recent Advances in Small Area Estimation with Applications and Evaluation of the Estimates
• Type: Topic Contributed
• Date/Time: Wednesday, August 2, 2017 : 2:00 PM to 3:50 PM
• Sponsor: Government Statistics Section
• Author(s): Carolina Franco* and William Bell and Serena Arima and Brunero Liseo and Gauri Datta
• Companies: U.S. Census Bureau and U.S. Census Bureau and Sapienza University, Rome and Sapienza University, Rome and University of Georgia and US Census Bureau
• Keywords: Small Area Estimation ; Measurement Error ; Errors in Variables ; Census Bureau ; Poverty ; Linear Mixed Models

Abstract

Area level models, such as the Fay-Herriot model, aim to improve direct survey estimates for small areas by borrowing strength from related covariates and from direct estimates across all domains. In their multivariate form, where related population characteristics are jointly modeled, area-level models allow for inference about functions of two or more characteristics, and may exploit dependence among the response variables to improve small area predictions. When model covariates are observed with random error, such as those drawn from another survey, it is important to account for this error in the modeling. We present a Bayesian analysis of a multivariate Fay-Herriot model with functional measurement error, allowing for both joint modeling of related characteristics and accounting for random observation error in some covariates. We apply it to estimating 2010-2011 changes in poverty rates of school-aged children for U.S. counties. For this application, the measurement error model results in great improvements in prediction when compared to the direct estimates, and ignoring the measurement error results in uncertainty estimates that are misleading.