Simultaneous Inference for Empirical Best Predictors with a Poverty Study in Small Areas

TL;DR

This paper develops simultaneous inference tools for empirical best predictors in generalized linear mixed models, enabling valid multiple comparisons across clusters, with applications to poverty studies in small areas.

Contribution

It introduces joint inference methods for empirical best predictors under generalized linear mixed models, filling a gap in tools for multiple comparisons in this domain.

Findings

Validated methods through extensive simulations.

Applied tools successfully to poverty rate prediction case study.

Demonstrated advantages over traditional inference approaches.

Abstract

Today, generalized linear mixed models are broadly used in many fields. However, the development of tools for performing simultaneous inference has been largely neglected in this domain. A framework for joint inference is indispensable to carry out statistically valid multiple comparisons of parameters of interest between all or several clusters. We therefore develop simultaneous confidence intervals and multiple testing procedures for empirical best predictors under generalized linear mixed models. In addition, we implement our methodology to study widely employed examples of mixed models, that is, the unit-level binomial, the area-level Poisson-gamma and the area-level Poisson-lognormal mixed models. The asymptotic results are accompanied by extensive simulations. A case study on predicting poverty rates illustrates applicability and advantages of our simultaneous inference tools.