Mixture Model and EM Algorithm in Small-Area Estimation

• Activity Number: 634
• Type: Topic Contributed
• Date/Time: Thursday, August 13, 2015 : 8:30 AM to 10:20 AM
• Sponsor: Survey Research Methods Section
• Author(s): Jiashen You* and Gauri S. Datta
• Companies: U.S. Census Bureau and University of Georgia/U.S. Census Bureau
• Keywords: small area estimation ; mixture model ; EM algorithm ; empirical Bayes

Abstract

Many generalized linear mixed models (GLM) for small-area estimation problems use only one parameter for model variance. The Fay-Herriot model and its many successors adopted this modeling structure for its relative simplicity in obtaining a theoretical derivation on the uncertainty of the estimator. However, this is also a major limitation for a small-area model. We study a small area model with a mixture of unknown variances. The standard Expectation-Maximization technique is applied to obtain empirical Bayes model estimates. We illustrate our findings through simulations and American Community Survey data.