A linearization for stable and fast geographically weighted Poisson regression

A - Papers appearing in refereed journals

Yoshida, T., Nakaya, T., Lu, B. and Harris, P. 2023. A linearization for stable and fast geographically weighted Poisson regression. International Journal Of Geographical Information Science. 37 (8), pp. 1818-1839. https://doi.org/10.1080/13658816.2023.2209811

AuthorsYoshida, T., Nakaya, T., Lu, B. and Harris, P.
Abstract

Although geographically weighted Poisson regression (GWPR) is a popular regression for spatially indexed count data, its development is relatively limited compared to that found for linear geographically weighted regression (GWR), where many extensions (e.g. multiscale GWR, scalable GWR) have been proposed. The weak development of GWPR can be attributed to the computational cost and identification problem in the underpinning Poisson regression model. This study proposes linearized GWPR (L-GWPR) by introducing a log-linear approximation into the GWPR model to overcome these bottlenecks. Because the L-GWPR model is identical to the Gaussian GWR model, it is free from the identification problem, easily implemented, computationally efficient, and offers similar potential for extension. Specifically, L-GWPR does not require a double-loop algorithm, which makes GWPR slow for large samples. Furthermore, we extended L-GWPR by introducing ridge regularization to enhance its stability (regularized L-GWPR). The results of the Monte Carlo experiments confirmed that regularized L-GWPR estimates local coefficients accurately and computationally efficiently. Finally, we compared GWPR and regularized L-GWPR through a crime analysis in Tokyo.

KeywordsIdentification problem; Ridge regression; Local coefficients; Log-linear approximation; Linearized geographically weighted Poisson regression
Year of Publication2023
JournalInternational Journal Of Geographical Information Science
Journal citation37 (8), pp. 1818-1839
Digital Object Identifier (DOI)https://doi.org/10.1080/13658816.2023.2209811
Open accessPublished as green open access
FunderBiotechnology and Biological Sciences Research Council
Funder project or codeS2N - Soil to Nutrition [ISPG]
Accepted author manuscript
Output statusPublished
Publication dates
Online12 May 2023
Publication process dates
Accepted28 Apr 2023
PublisherTaylor & Francis
ISSN1365-8816

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