Distance metric choice can both reduce and induce collinearity in geographically weighted regression

A - Papers appearing in refereed journals

Comber, A., Chi, K., Huy, M. Q., Nguyen, Q., Lu, B., Phe, H. H. and Harris, P. 2019. Distance metric choice can both reduce and induce collinearity in geographically weighted regression. Environment and Planning B: Urban Analytics and City Science. https://doi.org/10.1177/2399808318784017

AuthorsComber, A., Chi, K., Huy, M. Q., Nguyen, Q., Lu, B., Phe, H. H. and Harris, P.

This paper explores the impact of different distance metrics on collinearity in local regression models such as geographically weighted regression. Using a case study of house price data collected in Hà Nội, Vietnam, and by fully varying both power and rotation parameters to create different Minkowski distances, the analysis shows that local collinearity can be both negatively and positively affected by distance metric choice. The Minkowski distance that maximised collinearity in a geographically weighted regression was approximate to a Manhattan distance with (power = 0.70) with a rotation of 30°, and that which minimised collinearity was parameterised with power = 0.05 and a rotation of 70°. The results indicate that distance metric choice can provide a useful extra tuning component to address local collinearity issues in spatially varying coefficient modelling and that understanding the interaction of distance metric and collinearity can provide insight into the nature and structure of the data relationships. The discussion considers first, the exploration and selection of different distance metrics to minimise collinearity as an alternative to localised ridge regression, lasso and elastic net approaches. Second, it discusses the how distance metric choice could extend the methods that additionally optimise local model fit (lasso and elastic net) by selecting a distance metric that further helped minimise local collinearity. Third, it identifies the need to investigate the relationship between kernel bandwidth, distance metrics and collinearity as an area of further work.

KeywordsGeographically weighted regression - GWR; Distance metrics; Model fit; Collinearity; GWR
Year of Publication2019
JournalEnvironment and Planning B: Urban Analytics and City Science
Digital Object Identifier (DOI)https://doi.org/10.1177/2399808318784017
Open accessPublished as green open access
FunderBiotechnology and Biological Sciences Research Council
Natural Environment Research Council
Funder project or codeNewton Fellowship
Modelling and managing critical zone relationships between soil, water and ecosystem processes across the Loess Plateau
The North Wyke Farm Platform [2012-2017]
Accepted author manuscript
Output statusPublished
Publication dates
Online11 Jul 2018
Publication process dates
Accepted26 May 2018
Copyright licenseCC BY
PublisherSage Publishing

Permalink - https://repository.rothamsted.ac.uk/item/8489w/distance-metric-choice-can-both-reduce-and-induce-collinearity-in-geographically-weighted-regression

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