Poisson mixed modelsapplications to small area data

Abstract

Small area estimation deals with the estimation of parameters in small subsets (small areas) of a global population. In the small arcas, sample sizes are UBUallY too small since designa are developed for the original population. Conventional modelling to high levels of disaggregation has too much error. Arealevel Poi.sson mixed modela are useful tools for estimating discrete response variables in small arcas, since they can capture part of the variability not collected by the fixed effects. The basic Poi.sson mixed model is extended by incorporating first SAR(l) spatially correlated effects and second time effects. For the temporal extension, two models are considered depending on the assumed time correlation structure. The first model assumes that time effects are dis tributed independently, while the second model considers that they are distribu ted according to an AR(l) process. A spatio-temporal model including both spatial and time extensions is also stud.ied. Each model is fi tted by the method of moments and two predictors of functions of fixed and ra.ndom effects are obtained: the empirical best predictor (EBP) and a plug-in predictor. Several simulation experiments are carried out for empirically analysing the behaviour of the estimators. As accuracy measure of thc proposed EBPs, bootstrap mean squared error estimators are given. Finally, the developed methodology and software are applied in two fields of practica! interest: poverty mapping and forest fires.