Chapter

Modelling Multivariate Counts Varying Continuously in Space*

Alexandra M. Schmidt and Marco A. Rodríguez

in Bayesian Statistics 9

Published in print October 2011 | ISBN: 9780199694587
Published online January 2012 | e-ISBN: 9780191731921 | DOI: http://dx.doi.org/10.1093/acprof:oso/9780199694587.003.0020
Modelling Multivariate Counts Varying Continuously in Space*

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We discuss models for multivariate counts observed at fixed spatial locations of a region of interest. Our approach is based on a continuous mixture of independent Poisson distributions. The mixing component is able to capture correlation among components of the observed vector and across space through the use of a linear model of coregionalization. We introduce here the use of covariates to allow for possible non‐stationarity of the covariance structure of the mixing component. We analyse joint spatial variation of counts of four fish species abundant in Lake Saint Pierre, Quebec, Canada. Models allowing the covariance structure of the spatial random effects to depend on a covariate, geodetic lake depth, showed improved fit relative to stationary models.

Keywords: Animal Abundance; Anisotropy; Linear Model of Coregionalization; Non‐Stationarity; Poisson Log‐Normal Distribution; Random Effects

Chapter.  13018 words.  Illustrated.

Subjects: Probability and Statistics

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