Biostatistics · 2003 · 458 citations · 21 references
ComputingBiostatisticsSpatial AnalysisSpatial ModelingSpatial StatisticsBayesian Spatial AnalysisSpatial Data ModelsSpatial EconometricsSpatial Statistical ModelingChild Growth TrajectoriesConditional Autoregressive ModelsHierarchical Spatial ModelsMarkov Chain Monte Carlo InferenceMultivariate Spatial ModelingProper Conditional Autoregressive ModelsSpatial Autoregressive Models
Conditional autoregressive models have been widely used for spatial data analysis over the past decade, but most work has focused on univariate, improper specifications. The authors aim to develop proper multivariate conditional autoregressive models and apply them as second‑stage spatial effect specifications in hierarchical models. They construct proper multivariate CAR models by adding spatial autoregression parameters, extending Mardia’s framework with a novel parametric linear transformation, and demonstrate the approach on child‑growth and HLA‑B allele‑frequency data using full Bayesian MCMC inference. © 2000.
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.
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