Alleviating the effect of collinearity in geographically weighted regression

M. J. Bárcena, P. Menéndez, M. B. Palacios, F. Tusell

Research output: Contribution to journalArticleResearchpeer-review

20 Citations (Scopus)

Abstract

Geographically weighted regression (GWR) is a popular technique to deal with spatially varying relationships between a response variable and predictors. Problems, however, have been pointed out (see Wheeler and Tiefelsdorf in J Geogr Syst 7(2):161–187, 2005), which appear to be related to locally poor designs, with severe impact on the estimation of coefficients. Different remedies have been proposed. We propose two regularization methods. The first one is generalized ridge regression, which can also be seen as an empirical Bayes method. We show that it can be implemented using ordinary GWR software with an appropriate choice of the weights. The second one augments the local sample as needed while running GWR. We illustrate both methods along with ordinary GWR on an example of housing prices in the city of Bilbao (Spain) and using simulations.

Original languageEnglish
Pages (from-to)441-466
Number of pages26
JournalJournal of Geographical Systems
Volume16
Issue number4
DOIs
Publication statusPublished - Oct 2014
Externally publishedYes

Keywords

  • Geographically weighted regression
  • GWR
  • Shrinkage estimators
  • Spatial models

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