A Coregionalization Model to Assist the Selection Process of Local and Global Variables in Semi-parametric Geographically Weighted Poisson Regression

Abstract

Geographical distribution of health outcomes are influenced by socio-economic and environmental factors operating at different spatial scales. Geographical variations in relationships between them can be revealed with a semi-parametric geographically weighted poisson regression (sGWPR), which is a mixed model than can combine geographically varying and geographically constant parameters. To decide if a parameter associated with a variable should vary geographically or not, two models can be compared: a model where all parameters are allowed to vary geographically and a mixed model, where all but one (the parameter under evaluation) parameters are allowed to vary geographically. If the difference between Aikaike's Information Criteria (AICc) is larger than 2, the model with lower AICc is selected. However, delivering model selection exclusively to AICc measure might hide important details in spatial variations of ecological associations, especially in situations where the difference between models is marginal. We propose to assist the decision by using a linear model of coregionalization (LMC), a geostatistical tool originally developed for geosciences. Here we show how the LMC can refine sGWPR analysis on ecological associations between socio-economic and environmental variables and low birth weight outcomes in the west north central region of Portugal.