A two-component normal mixture alternative to the Fay-Herriot model

Abstract: This article considers a robust hierarchical Bayesian approach to deal with random effects of small area means when some of these effects assume extreme values, resulting in outliers. In presence of outliers, the standard Fay-Herriot model, used for modeling area-level data, under normality assumptions of the random effects may overestimate random effects variance, thus provides less than ideal shrinkage towards the synthetic regression predictions and inhibits borrowing information. Even a small number of substantive outliers of random effects result in a large estimate of the random effects variance in the Fay-Herriot model, thereby achieving little shrinkage to the synthetic part of the model or little reduction in posterior variance associated with the regular Bayes estimator for any of the small areas. While a scale mixture of normal distributions with known mixing distribution for the random effects has been found to be effective in presence of outliers, the solution depends on the mixing distribution. As a possible alternative solution to the problem, a two-component normal mixture model has been proposed based on noninformative priors on the model variance parameters, regression coefficients and the mixing probability. Data analysis and simulation studies based on real, simulated and synthetic data show advantage of the proposed method over the standard Bayesian Fay-Herriot solution derived under normality of random effects.