Spatial autoregressive models for areal data within gamlss

Abstract

In spatial data analysis the data are indexed by a set of locations in space, the way this set is defined separates spatial statistics into three areas: Geostatistics, models for Areal data, and Point Process. In this work we will focus on the models for areal data, specifically in the simultaneous autoregressive (SAR) models, which has applications in many fields such as Ecology, Public Health, Texture Analysis and Spatial Econometrics. It is proposed to implement the SAR models within the generalized additive models for location, scale, and shape (GAMLSS), allowing to consider any type of distribution to fit the data, and to model all the parameters of a distributions as function of the explanatory variables. The implementation of this procedure within GAMLSS is made considering the connection between random effects and penalized smoothers, and the relationship of the SAR and conditional autoregressive (CAR) models. An efficient algorithm was implemented to construct the penalty matrix compatible with general scope of penalization methods. Monte Carlo simulation studies were conducted with the purpose of evaluating the properties of the regression coefficients estimators of the SAR-GAMLSS models in the context of finite samples and with different probability distributions for the response variable. The methodology was applied to the analysis of house prices and also to the study of income inequality in the State of Pernambuco, Brazil, considering the spatial structure of the regions in the analysis.