Empirical Best Prediction of Small Area Means Based on a Unit-Level Gamma-Poisson Model

Abstract

Existing small area estimation procedures for count data have important limitations. For instance, an M-quantile-based method is known to be less efficient than model-based procedures if the assumptions of the model hold. Also, frequentist inference procedures for Poisson generalized linear mixed models can be computationally intensive or require approximations. Furthermore, area-level models are incapable of incorporating unit-level covariates. We overcome these limitations by developing a small area estimation procedure for a unit-level gamma-Poisson model. The conjugate form of the model permits computationally simple estimation and prediction procedures. We obtain a closed-form expression for the empirical best predictor of the mean as well as a closed-form mean square error estimator. We validate the procedure through simulations. We illustrate the proposed method using a subset of data from the Iowa Seat-Belt Use survey.