ABSTRACT
In the analysis of spatially configured data, positive covariation is typically expected between observations that are close to each other, so that residual spatial dependence may remain under a simple iid residual assumption. Spatial heterogeneity in regression relationships is also common. Modelling area differences or point patterns with spatially structured effects reflects the empirical regularity that neighbouring areas or points tend to be similar, and that similarity typically diminishes as distance increases. A widely used scheme, especially in spatial econometrics, specifies the joint density via simultaneous autoregressive or spatial autoregressive effects. The spatially adaptive approach retains the principle of spatial borrowing of strength, but modifies it to better represent discontinuities in the outcome and/or observed risk factors. The Gaussian Markov random field approximation involves a triangulation of the spatial domain, and the density of the triangulation mesh determines how close the approximation is.
