Estimation of the proportion of overweight individuals in small areas—a robust extension of the Fay–Herriot model

Hierarchical model such as Fay–Herriot (FH) model is often used in small area estimation. The method might perform well overall but is vulnerable to outliers. We propose a robust extension of the FH model by assuming the area random effects follow a t distribution with an unknown degrees-of-freedom parameter. The inferences are constructed using a Bayesian framework. Monte Carlo Markov Chain (MCMC) such as Gibbs sampling and Metropolis–Hastings acceptance and rejection algorithms are used to obtain the joint posterior distribution of model parameters. The procedure is used to estimate the county-level proportion of overweight individuals from the 2003 public-use Behavioral Risk Factor Surveillance System (BRFSS) data. We also discuss two approaches for identifying outliers in the context of this application. Copyright © 2006 John Wiley & Sons, Ltd.