Robust generalized linear mixed models for small area estimation

Use of generalized linear model for small area estimation is relatively new for the survey statisticians. For a unified analysis of both discrete and continuous data, this paper introduces hierarchical Bayes generalized mixed linear models. Constant variance normal distribution is usually assumed for small area specific random effects. This paper uses, instead, a finite mixture of normals as a prior for the random effects. Such prior is believed to be more robust than a normal prior. There are difficulties with this model, however. First, standard reference priors for the parameters of the mixture components yield improper posteriors. Second, posterior analysis does not provide a direct estimate of the number of components to be used for the mixture distribution. Both improper and partially proper prior distributions are used and a general theorem is provided to ensure the propriety of posteriors. The hierarchical Bayes procedure is implemented via Markov Chain Monte Carlo integration techniques. (C) 2001 Elsevier Science B.V. All rights reserved.