A Hierarchical Bayes Generalization of the Fay-Herriot Method to Unit Level Nonlinear Mixed Models for Small Area Estimation

• Activity Number: 386
• Type: Contributed
• Date/Time: Thursday, August 15, 2002 : 8:30 AM to 10:20 AM
• Sponsor: Section on Survey Research Methods*
• Author(s): Akhil Vaish*+ and Avinash Singh and Ralph Folsom
• Affiliation(s): RTI International and RTI International and RTI International
• Keywords: Estimating functions ; Pseudo Score Functions ; Survey weighted HB ; MCMC

Abstract

We consider the pioneering work of Fay and Herriot (FH) (1979) on empirical Bayes small area estimation (SAE) with survey data and some of its limitations. In an attempt to overcome the limitations, a generalization of the FH solution to unit-level nonlinear mixed models is presented. Like FH, it employs data aggregation through survey-weighted estimating functions (EFs) rather than through estimators and has several advantages over the FH approach. EFs can better be approximated by Normal distributions even for modest sample sizes, can also be based on unit-level covariate information, and can be specified at the lowest level of aggregation to avoid the problem of internal inconsistency. For hierarchical Bayes (HB) SAE, the proposed approach simply replaces the likelihood computed under the assumption of ignorable design with the EF based Gaussian likelihood which does not require ignorability of the design.

The method is illustrated by a simple simulation study where a HB linear mixed model is fitted to the data obtained from a nonignorable sample design. Both fixed and random parameters are estimated to construct small area estimates. MCMC is used for HB parameter estimation.