Nonlinear generalized spatial conditional overdispersion models extensions proposals

Mabel Morales-Otero, University of Navarra

Co-authors: Maria Durban, Universidad Carlos III de Madrid; Vicente Núñez-Antón, University of the Basque Country

Abstract: Generalized spatial conditional overdispersion models for spatial count data allow dispersion to vary according to covariates and/or spatial terms, where linear relationships between the model’s covariates and the mean or the dispersion of the response is assumed. However, they could be given by another, maybe a nonlinear, pattern. We propose a semiparametric extension of these models to capture potential nonlinear relationships. More specifically, we incorporate $P$-splines, in their mixed model representation, to smooth the effects of selected covariates in the model. We analyse infant mortality rates and mother’s postnatal period screening test in Colombia and find evidence of the existence of a nonlinear relationship between infant mortality rates and the variable representing the amount of resources provided by the government for education.