Pseudo hierarchical Bayes small area estimation combining unit level models and survey weights

Abstract

Unit level random effects models, such as nested error regression models, are often used in small area estimation to obtain efficient model-based estimators of small area means. Such estimators typically do not make use of the survey weights. As a result, the estimators are not design consistent unless the sampling design is self-weighting within areas. In this paper, a two-step approach is developed to obtain design-consistent small area estimates by utilizing the survey weights. In the first step, conditional posterior means and conditional posterior variances of the small area means are derived from the aggregated area level model, assuming that the variance components and regression parameters (fixed effects) are known. In the second step, posterior estimates of the variance components are obtained from the unit level model. Three different methods of estimating the regression parameters are studied. Combining the two estimation steps leads to pseudo-hierarchical Bayes estimators for the small area means. The proposed methods are evaluated on a real data set studied by Battese et al. (J. Amer. Statist. Assoc. 83 (1988) 28).