Old and New Approaches for Spatially Varying Coefficient Models

This note compares old and new methods for modeling spatial heterogeneity with spatially varying parameter (SVP) models. Older methods considered include spatial expansion, spatial adaptive filtering, and geographically weighted regression. Newer methods that have emerged since the beginning of the 21st include smooth transition autoregression, spatial Gaussian process, and random parameter models with autoregressive processes. A simulation is used to graphically demonstrate differences between the approaches. Regional scientists planning on using any one of these approaches should carefully consider whether the data generating process they are working with is consistent with the assumptions an SVP maintains regarding spatial heterogeneity.