The importance of scale in spatially varying coefficient modelling

A - Papers appearing in refereed journals

Murakami, D., Lu, B., Harris, P., Brunsdon, C., Charlton, M., Nakaya, T. and Griffith, D. A. 2019. The importance of scale in spatially varying coefficient modelling. Annals of the American Association of Geographers. 109 (1), pp. 50-70.

AuthorsMurakami, D., Lu, B., Harris, P., Brunsdon, C., Charlton, M., Nakaya, T. and Griffith, D. A.

While 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: (i) geographically weighted regression (GWR) with a fixed distance or (ii) an adaptive distance bandwidth (GWRa),(iii) flexible bandwidth GWR (FB-GWR) with fixed distance or (iv) adaptive distance bandwidths (FB-GWRa), (v) eigenvector spatial filtering (ESF), and (vi) 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 naively 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 fixedbandwidth counterparts (GWR and FB-GWR).

KeywordsNon-stationarity; Spatial scale; Flexible bandwidth geographically weighted regression; Random effects eigenvector spatial filtering; Monte Carlo simulation
Year of Publication2019
JournalAnnals of the American Association of Geographers
Journal citation109 (1), pp. 50-70
Digital Object Identifier (DOI)
Open accessPublished as green open access
FunderBiotechnology and Biological Sciences Research Council
National Natural Science Foundation of China
Funder project or codeThe North Wyke Farm Platform [2012-2017]
The North Wyke Farm Platform- National Capability [2017-22]
S2N - Soil to Nutrition - Work package 2 (WP2) - Adaptive management systems for improved efficiency and nutritional quality
S2N - Soil to Nutrition - Work package 3 (WP3) - Sustainable intensification - optimisation at multiple scales
Accepted author manuscript
Output statusPublished
Publication dates
Online20 Dec 2018
Publication process dates
Accepted01 Feb 2018
Copyright licensePublisher copyright
PublisherRoutledge Journals, Taylor & Francis Ltd

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