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.
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Notes
In this connection, we notice that the bi-square kernel has been replaced by a Gaussian kernel as the default option in the R function gwr of package spgwr (Bivand and Yu 2012) that we use in some of the computations below.
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Acknowledgments
The comments of the editor of the journal and three referees have substantially improved the original manuscript and are gratefully acknowledged. Partial support from grants ECO2008-05622 (MCyT) and IT-347-10 (Basque Government) is gratefully acknowledged.
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Bárcena, M.J., Menéndez, P., Palacios, M.B. et al. Alleviating the effect of collinearity in geographically weighted regression. J Geogr Syst 16, 441–466 (2014). https://doi.org/10.1007/s10109-014-0199-6
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DOI: https://doi.org/10.1007/s10109-014-0199-6