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Biostatistics 4:11-15 (2003)
© 2003 Oxford University Press

Proper multivariate conditional autoregressive models for spatial data analysis

Alan E. Gelfand{dagger} and Penelope Vounatsou

Department of Statistics, University of Connecticut, Storrs, USA alan{at}stat.uconn.edu
Swiss Tropical Institute, Socinstrasse 57, Basle, Switzerland

{dagger}To whom correspondence should be addressed

In the past decade conditional autoregressive modelling specifications have found considerable application for the analysis of spatial data. Nearly all of this work is done in the univariate case and employs an improper specification. Our contribution here is to move to multivariate conditional autoregressive models and to provide rich, flexible classes which yield proper distributions. Our approach is to introduce spatial autoregression parameters. We first clarify what classes can be developed from the family of Mardia (1988) and contrast with recent work of Kim et al. (2000). We then present a novel parametric linear transformation which provides an extension with attractive interpretation. We propose to employ these models as specifications for second-stage spatial effects in hierarchical models. Two applications are discussed; one for the two-dimensional case modelling spatial patterns of child growth, the other for a four-dimensional situation modelling spatial variation in HLA-B allele frequencies. In each case, full Bayesian inference is carried out using Markov chain Monte Carlo simulation.

Keywords: Gene frequencies; Hierarchical model; Markov chain Monte Carlo simulation; Model choice; Nutritional indicators; Spatial regression parameter


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