In recent years, more and more data are becoming available on the more disparate phenomena in a geo-referenced form and multivariate spatial data sets are becoming increasingly popular. Until now, however, attention has been paid mainly to the investigation of univariate spatial distributions. For instance, in the investigation of spatial variation in disease rates, standard epidemiological mapping methods have so far almost entirely focused on the spatial modelling of single diseases, that is, on single univariate spatial distributions of cases. Many diseases, however, show similar patterns of geographical variation which may suggest the existence of common underlying "factors" responsible for differences in risk. In this work we propose a multivariate spatial modelling framework for the study of spatial phenomena when the information are provided by frequency tables which are geo-referenced in a "geostatistical" fashion. For a given set of idealized pointwise spatial locations, we will assume to observe a set of counts in the N cells of a given, in general multi-way, contingency table. In an epidemiological study, frequency counts might be collected for idealized districts with the same population size. For instance, categorical data might be collected for the patients of a group of family practitioner, which in Italy have roughly the same number of patients, spatially geo-referenced by the addresses of the practitioner surgeries. Following the proposals in the literature made in the univariate case for non-Gaussian data, in this work we present a statistical modelling framework based on a hierarchical multivariate spatial model where the latent structure is given by a Gaussian geostatistical spatial factor model. The methodology proposed can be seen as an extension of the geostatistical linear model of coregionalization, and of the related "factorial kriging analysis", to the case of geo-referenced contingency tables.
Modelling geo-referenced categorical data: a multivariate geostatistical approach
MINOZZO, Marco
2003-01-01
Abstract
In recent years, more and more data are becoming available on the more disparate phenomena in a geo-referenced form and multivariate spatial data sets are becoming increasingly popular. Until now, however, attention has been paid mainly to the investigation of univariate spatial distributions. For instance, in the investigation of spatial variation in disease rates, standard epidemiological mapping methods have so far almost entirely focused on the spatial modelling of single diseases, that is, on single univariate spatial distributions of cases. Many diseases, however, show similar patterns of geographical variation which may suggest the existence of common underlying "factors" responsible for differences in risk. In this work we propose a multivariate spatial modelling framework for the study of spatial phenomena when the information are provided by frequency tables which are geo-referenced in a "geostatistical" fashion. For a given set of idealized pointwise spatial locations, we will assume to observe a set of counts in the N cells of a given, in general multi-way, contingency table. In an epidemiological study, frequency counts might be collected for idealized districts with the same population size. For instance, categorical data might be collected for the patients of a group of family practitioner, which in Italy have roughly the same number of patients, spatially geo-referenced by the addresses of the practitioner surgeries. Following the proposals in the literature made in the univariate case for non-Gaussian data, in this work we present a statistical modelling framework based on a hierarchical multivariate spatial model where the latent structure is given by a Gaussian geostatistical spatial factor model. The methodology proposed can be seen as an extension of the geostatistical linear model of coregionalization, and of the related "factorial kriging analysis", to the case of geo-referenced contingency tables.
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