Hierachical Bayes Prediction in log-transformed Linear Mixed Model with Applications to Small Area Estimation

In this paper we study a very basic Small Area model, the Battese-Harter-Fuller, applied to a log-transformed variable and adopt a reference Hierarchical Bayes approach to obtain estimates of finite population Small Area means. With reference Hierarchical Bayesian analysis we mean an analysis in which reference, non-informative priors for unknown parameters are assumed and estimation is implemented by means of Markov Chain Monte Carlo softwares such as OpenBugs (Thomas et al., 2006). One advantage of Hierarchical Bayes approach is that it can easily take into account all sources of variability. This should lead to measure of uncertainty of predicted Small Area means that consider also the variability involved by the estimation of variance components