Additive Random Coefficient (ARC) Models for Robust Small Area Estimation

• Activity Number: 174
• Type: Contributed
• Date/Time: Monday, August 1, 2011 : 10:30 AM to 12:20 PM
• Sponsor: Section on Survey Research Methods
• Author(s): Ralph E. Folsom*+ and Akhil K. Vaish and Avinash C. Singh
• Companies: RTI International and RTI International and NORC at the The University of Chicago
• Keywords: small area estimation ; generalized design effects ; nonignorable survey sampling design ; general liner mixed model ; additive random coefficient ; survey weighted estimating equations

Abstract

Unit or person-level ARC models with linear, logistic, and log-linear marginal mean functions are developed for small area estimation. ARC models take the form of a first order Taylor series approximation to the associated general linear mixed model. The area-level random coefficient vectors specify effects for demographic groups. Protection against nonignorable sample designs is provided by a hybrid solution that combines the marginal [probability (P) sampling plus ARC model (?) ] distribution of the fixed regression coefficients with the MCMC simulated Bayes posterior distributions for the small area specific random coefficient vectors. Survey weighted estimating equations are employed in the solution for the fixed and random coefficients along with sample design consistent covariance matrix estimators. A generalized design effect matrix is used to stabilize the area-level covariance matrices for the random coefficients. A simulation study for the logistic ARC model contrasts the new method's performance with a nonlinear version of You and Rao's (2003) pseudo hierarchical Bayes solution that discounts the effect of nonignorable samples on the mean squared errors of estimates.