Exploring geometric anisotropy for point-referenced spatial data

Isotropic covariance functions are routinely adopted in specifying models for point-referenced spatial data but carry the limitation that spatial dependence is not directional. Geometric anisotropic covariance functions offer a class of stationary specifications which incorporate directional dependence through spatial range. They have received modest attention in the literature but can provide flexible and readily interpretable directional dependence. Within a Bayesian framework, this paper attempts to illuminate when and how much such models for random effects in geostatistical settings improve out-of-sample predictive performance. We show that geometric anisotropy yields better predictive performance when the residuals strongly depart from isotropy (anisotropy ratio is much greater than one) and sample size is fairly large. Also, improvement is more prominent when the spatial variance is much greater than the pure error variance. The investigation of predictive performance is illustrated through simulation as well as modeling of real data on PM2.5 monitoring stations.