Multivariate Spatial Models

Authored by: Sudipto Banerjee

Handbook of Spatial Epidemiology

Print publication date:  April  2016
Online publication date:  April  2016

Print ISBN: 9781482253016
eBook ISBN: 9781482253023
Adobe ISBN:


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This chapter deals with multivariate spatial modeling. Spatial data are often multivariate in the sense that multiple (i.e., more than one) outcomes are measured at each spatial unit. As in the univariate case, the spatial units can be referenced by points or by areal units. Multivariate areal data are conspicuous in public health, where each county or administrative unit supplies counts or rates for a number of diseases. For example, epidemiologists often encounter measurements on several diseases from each spatial unit (e.g., county) and wish to account for dependence among the different diseases, as well as the spatial dependence between sites. The natural and environmental sciences are teeming with examples of multivariate point-referenced data. For example, in ambient air quality assessment, we seek to jointly model multiple contaminants (e.g., ozone, nitric oxide, carbon monoxide, and PM2.5) at a fixed set of monitoring sites. Inference focuses upon three major aspects: (1) estimating associations among the contaminants, (2) estimating the strength of spatial association for each contaminant, and (3) predicting the contaminants at arbitrary locations. We will first treat multivariate areal data and then attend to point-referenced data.

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