Spatial Modeling With Spatially Varying Coefficient Processes

TLDR

Regression models for spatially correlated responses often assume constant coefficients, yet many applications require coefficients that vary locally within the region. This study focuses on modeling spatially varying coefficients at the local level. The authors model coefficient surfaces as realizations of spatial processes, formalizing this for Gaussian responses and extending the approach to generalized linear models and spatio‑temporal settings. They demonstrate static and dynamic spatially varying coefficient models using a dataset of log house prices.

Abstract

In many applications, the objective is to build regression models to explain a response variable over a region of interest under the assumption that the responses are spatially correlated. In nearly all of this work, the regression coefficients are assumed to be constant over the region. However, in some applications, coefficients are expected to vary at the local or subregional level. Here we focus on the local case. Although parametric modeling of the spatial surface for the coefficient is possible, here we argue that it is more natural and flexible to view the surface as a realization from a spatial process. We show how such modeling can be formalized in the context of Gaussian responses providing attractive interpretation in terms of both random effects and explaining residuals. We also offer extensions to generalized linear models and to spatio-temporal setting. We illustrate both static and dynamic modeling with a dataset that attempts to explain (log) selling price of single-family houses.