Comparison of Small Area Procedures based on Gamma Distributions with Extension to Informative Sampling

TL;DR

This paper compares gamma distribution-based small area prediction models, introduces an extension for informative sampling, and evaluates their performance through simulations and real data application.

Contribution

It provides a formal comparison of gamma-gamma and generalized linear mixed models for small area prediction and extends the gamma-gamma model to informative sampling.

Findings

Gamma-gamma model shows favorable properties in simulations.

Bias-corrected mean square error estimators improve prediction accuracy.

Extension to informative sampling enhances model applicability.

Abstract

The gamma distribution is a useful model for small area prediction of a skewed response variable. We study the use of the gamma distribution for small area prediction. We emphasize a model, called the gamma-gamma model, in which the area random effects have gamma distributions. We compare this model to a generalized linear mixed model. Each of these two models has been proposed independently in the literature, but the two models have not yet been formally compared. We evaluate the properties of two mean square error estimators for the gamma-gamma model, both of which incorporate corrections for the bias of the estimator of the leading term. Finally, we extend the gamma-gamma model to informative sampling. We conduct thorough simulation studies to assess the properties of the alternative predictors. We apply the proposed methods to data from an agricultural survey.