The Importance of Scale in Spatially Varying Coefficient Modeling

Daisuke Murakami, Binbin Lu, Paul Harris, Chris Brunsdon, Martin Charlton, Tomoki Nakaya, Daniel A. Griffith

Research output: Contribution to journalArticlepeer-review

55 Citations (Scopus)


Although spatially varying coefficient (SVC) models have attracted considerable attention in applied science, they have been criticized as being unstable. The objective of this study is to show that capturing the “spatial scale” of each data relationship is crucially important to make SVC modeling more stable and, in doing so, adds flexibility. Here, the analytical properties of six SVC models are summarized in terms of their characterization of scale. Models are examined through a series of Monte Carlo simulation experiments to assess the extent to which spatial scale influences model stability and the accuracy of their SVC estimates. The following models are studied: (1) geographically weighted regression (GWR) with a fixed distance or (2) an adaptive distance bandwidth (GWRa); (3) flexible bandwidth GWR (FB-GWR) with fixed distance or (4) adaptive distance bandwidths (FB-GWRa); (5) eigenvector spatial filtering (ESF); and (6) random effects ESF (RE-ESF). Results reveal that the SVC models designed to capture scale dependencies in local relationships (FB-GWR, FB-GWRa, and RE-ESF) most accurately estimate the simulated SVCs, where RE-ESF is the most computationally efficient. Conversely, GWR and ESF, where SVC estimates are naïvely assumed to operate at the same spatial scale for each relationship, perform poorly. Results also confirm that the adaptive bandwidth GWR models (GWRa and FB-GWRa) are superior to their fixed bandwidth counterparts (GWR and FB-GWR). Key Words: flexible bandwidth geographically weighted regression, Monte Carlo simulation, nonstationarity, random effects eigenvector spatial filtering, spatial scale.

Original languageEnglish
Pages (from-to)50-70
Number of pages21
JournalAnnals of the American Association of Geographers
Issue number1
Publication statusPublished - 2019 Jan 2


  • Monte Carlo simulation
  • flexible bandwidth geographically weighted regression
  • nonstationarity
  • random effects eigenvector spatial filtering
  • spatial scale

ASJC Scopus subject areas

  • Geography, Planning and Development
  • Earth-Surface Processes


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