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The Importance of Scale in Spatially Varying Coefficient Modeling

Author

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

Abstract

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.

Suggested Citation

  • Daisuke Murakami & Binbin Lu & Paul Harris & Chris Brunsdon & Martin Charlton & Tomoki Nakaya & Daniel A. Griffith, 2019. "The Importance of Scale in Spatially Varying Coefficient Modeling," Annals of the American Association of Geographers, Taylor & Francis Journals, vol. 109(1), pages 50-70, January.
    • Handle: RePEc:taf:raagxx:v:109:y:2019:i:1:p:50-70
    DOI: 10.1080/24694452.2018.1462691
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    Citations

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    Cited by:

    1. Paul Harris & Bruno Lanfranco & Binbin Lu & Alexis Comber, 2020. "Influence of Geographical Effects in Hedonic Pricing Models for Grass-Fed Cattle in Uruguay," Agriculture, MDPI, vol. 10(7), pages 1-17, July.
    2. Burhan Can Karahasan & Mehmet Pinar, 2023. "Climate change and spatial agricultural development in Turkey," Review of Development Economics, Wiley Blackwell, vol. 27(3), pages 1699-1720, August.
    3. Pengyu Liu & Chao Wu & Miaomiao Chen & Xinyue Ye & Yunfei Peng & Sheng Li, 2020. "A Spatiotemporal Analysis of the Effects of Urbanization’s Socio-Economic Factors on Landscape Patterns Considering Operational Scales," Sustainability, MDPI, vol. 12(6), pages 1-15, March.
    4. Chen, Feng & Mei, Chang-Lin, 2021. "Scale-adaptive estimation of mixed geographically weighted regression models," Economic Modelling, Elsevier, vol. 94(C), pages 737-747.
    5. Li Gao & Mingjing Huang & Wuping Zhang & Lei Qiao & Guofang Wang & Xumeng Zhang, 2021. "Comparative Study on Spatial Digital Mapping Methods of Soil Nutrients Based on Different Geospatial Technologies," Sustainability, MDPI, vol. 13(6), pages 1-19, March.
    6. Taylor M. Oshan & Levi J. Wolf & Mehak Sachdeva & Sarah Bardin & A. Stewart Fotheringham, 2022. "A scoping review on the multiplicity of scale in spatial analysis," Journal of Geographical Systems, Springer, vol. 24(3), pages 293-324, July.

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