Area-level spatio-temporal Poisson mixed models for predicting domain counts and proportions

TL;DR

This paper develops area-level spatio-temporal Poisson mixed models with spatial and temporal correlations to improve prediction of counts and proportions in small areas, demonstrated through forest fire and poverty data in Galicia.

Contribution

It introduces new spatio-temporal Poisson mixed models with SAR(1) spatial effects for small area prediction of counts and proportions, with estimation of mean squared errors via bootstrap.

Findings

Effective modeling of forest fire counts in Galicia.

Accurate estimation of poverty proportions among women.

Models outperform traditional methods in predictive accuracy.

Abstract

This paper introduces area-level Poisson mixed models with temporal and SAR(1) spatially correlated random effects. Small area predictors of the proportions and counts of a dichotomic variable are derived from the new models and the corresponding mean squared errors are estimated by parametric bootstrap. The paper illustrates the introduced methodology with two applications to real data. The first one deals with data of forest fires in Galicia (Spain) during 2007-2008 and the target is modeling and predicting counts of fires. The second one treats data from the Spanish living conditions survey of Galicia of 2013 and the target is the estimation of county proportions of women under the poverty line.