Abstract
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.
Highlights
Recent advances in computing and software have renewed interest in using local regression methods (LRM) to model spatial heterogeneity
An important point to note about the spatial adaptive filter (SAF) figure is that there is no compelling reason for explaining the observed patterns, whereas with the spatial expansion method, a polynomial surface is consistent with the quadratic expansion of (x, y)-coordinate terms
Regional scientists are in a unique position to contribute to the advancement of spatially varying parameter models, given the spatially inherent nature of the data we use
Summary
Recent advances in computing and software have renewed interest in using local regression methods (LRM) to model spatial heterogeneity. This note uses simulation to compare graphically earlier LRM, including Casetti (1972)’s spatial expansion model, Foster and Gorr (1982)’s spatial adaptive filter (SAF), and Cleveland and Devlin (1988)’s geographically weighted regression (GWR), with more recent LRM. This article was the Presidential Address of the 60th Southern Regional Science Association annual meeting. (c) Southern Regional Science Association 2021 ISSN 1553-0892, 0048-49X (online) www.srsa.org/rrs. LRM are intuitively appealing and most are relatively easy to estimate, but researchers should use caution when selecting which LRM is suitable for a problem at hand. Researchers considering using LRM should consider using an exploratory approach to choose a LRM by carefully comparing the in-sample performance of each method
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