Title: On modelling and estimating geo-referenced count spatial data with excessive zeros
Authors: Diego Morales Navarrete - Pontificia Universidad Catolica de Chile (Ecuador) [presenting]
Luis Mauricio Castro - Pontificia Universidad Catolica de Chile (Chile)
Moreno Bevilacqua - Universidad de Valparaiso (Chile)
Christian Caamano Carrillo - Universidad del Bío-Bío (Chile)
Abstract: Modelling spatial data is a challenging task in statistics. In many applications, the observed data can be modelled using Gaussian, skew-Gaussian, or even restricted random field models. However, in several fields, such as population genetics, epidemiology, and population dynamics, the data of interest are counts with excess of zeros in some cases, and therefore the mentioned models are not suitable for their analysis. Consequently, there is a need for spatial models that can adequately describe data coming from counting processes and handle the excess of zeros in data. Three approaches are commonly used to model this type of data, namely, GLMMs with Gaussian random field (GRF) effects, hierarchical models, and copula models. Unfortunately, these approaches do not explicitly characterize the random field like their q-dimensional distribution or correlation function. It is important to stress that GLMMs and hierarchical models induce a discontinuity in the path. Here, we propose a novel approach to efficiently and accurately model spatial count data with excess of zeros to deal with this. This approach is based on a random field characterization for count data with excess of zeros that inherit some well-known geometric properties from GFRs.