Encapsulating Spatially Varying Relationships with a Generalized Additive Model

A - Papers appearing in refereed journals

Comber, A., Harris, P., Murakami, D., Nakaya, T., Tsutsumida, N., Yoshida, T. and Brunsdon, C. 2024. Encapsulating Spatially Varying Relationships with a Generalized Additive Model. ISPRS International Journal of Geo-Information. 13 (12), p. 459. https://doi.org/10.3390/ijgi13120459

AuthorsComber, A., Harris, P., Murakami, D., Nakaya, T., Tsutsumida, N., Yoshida, T. and Brunsdon, C.
Abstract

Abstract: This paper describes the use of Generalized Additive Models (GAMs) to create regression models whose coefficient estimates vary with geographic location—spatially varying coefficient (SVC) models. The approach uses Gaussian Process (GP) splines (smooths) for each predictor variable,
which are parameterised with observation location in order to generate SVC estimates. These describe the spatially varying relationships between predictor and response variables. The proposed GAM approach was compared with Multiscale Geographically Weighted Regression (MGWR) using simulated data with complex spatial heterogeneities. The geographical GP GAM (GGP-GAM) was found to out-perform MGWR across a range of fit metrics and resulted in more accurate coefficient
estimates and lower residual errors. One of the GGP-GAM models was investigated in detail to illustrate model diagnostics, checks of spline/smooth convergence and basis evaluations. A larger simulated case study was investigated to explore the trade-offs between GGP-GAM complexity (via
the number of knots), performance and computational efficiency. Finally, the GGP-GAM and MGWR approaches were applied to an empirical case study. The resulting models had very similar accuracies and fits and generated subtly different spatially varying coefficient estimates. A number of areas of further work are identified.

KeywordsSpatial analysis; GAM; Spatial regression; Process spatial heterogeneity
Year of Publication2024
JournalISPRS International Journal of Geo-Information
Journal citation13 (12), p. 459
Digital Object Identifier (DOI)https://doi.org/10.3390/ijgi13120459
Web address (URL)https://doi.org/10.3390/ijgi13120459
Open accessPublished as ‘gold’ (paid) open access
FunderBiotechnology and Biological Sciences Research Council
Funder project or codeResilient Farming Futures (WP3): Digital platforms for supporting national agroecosystem ‘resilience’ through systems adaptations
Publisher's version
Accepted author manuscript
Output statusPublished
Publication dates
Online19 Dec 2024
Publication process dates
Accepted13 Dec 2024
PublisherMDPI
ISSN2220-9964

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