Living with Collinearity in Local Regression Models

Living with Collinearity in Local Regression Models
Chris Brunsdon1, Martin Charlton2 and Paul Harris2

1.People, Space and Place, Roxby Building, University of Liverpool, L69 7ZT, UK (Christopher.Brunsdon@liverpool.ac.uk)
2.National Centre for Geocomputation, National University of Ireland Maynooth, Maynooth, Co. Kildare, Ireland (Martin.Charlton@nuim.ie; Paul.Harris@nuim.ie)

Abstract: In this study, we investigate the issue of local collinearity in the predictor data when using geographically weighted regression (GWR) to explore spatial relationships between response and predictor variables. Here we show how the ideas of condition numbers and variance inflation factors may be `localised’ to detect and respond to problems caused by this phenomenon. Furthermore, we introduce two adapted forms of GWR where localised regressions that are resistant to collinearity effects are specified only at locations where collinearity is considered detrimental to the standard local fit. We present initial findings via the use of a simulation study designed to assess the sensitivity of GWR outputs to various levels of collinearity. This study aims to build upon, and respond to, recent research in this area.

Keywords: Geographically Weighted Regression, Variance Inflation Factor, Condition Number, Ridge Regression

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