Geographically weighted regression with parameter-specific distance metrics

ABSTRACT

Geographically weighted regression (GWR) is an important local technique to model spatially varying relationships. A single distance metric (Euclidean or non-Euclidean) is generally used to calibrate a standard GWR model. However, variations in spatial relationships within a GWR model might also vary in intensity with respect to location and direction. This assertion has led to extensions of the standard GWR model to mixed (or semiparametric) GWR and to flexible bandwidth GWR models. In this article, we present a strongly related extension in fitting a GWR model with parameter-specific distance metrics (PSDM GWR). As with mixed and flexible bandwidth GWR models, a back-fitting algorithm is used for the calibration of the PSDM GWR model. The value of this new GWR model is demonstrated using a London house price data set as a case study. The results indicate that the PSDM GWR model can clearly improve the model calibration in terms of both goodness of fit and prediction accuracy, in contrast to the model fits when only one metric is singly used. Moreover, the PSDM GWR model provides added value in understanding how a regression model’s relationships may vary at different spatial scales, according to the bandwidths and distance metrics selected. PSDM GWR deals with spatial heterogeneities in data relationships in a general way, although questions remain on its model diagnostics, distance metric specification, and computational efficiency, providing options for further research.

KEYWORDS:

• GWR
• GWmodel
• local regression
• spatial heterogeneity
• model anisotropy

Acknowledgments

Research presented in this paper was jointly supported by projects from the National Natural Science Foundation of China [NSFC: 41401455], [NSFC: U1533102]; an open research fund of State Key Laboratory of Information Engineering in Surveying, Mapping and Remote Sensing (No. 14I01); an open research fund by State Key Laboratory of Resources and Environmental Information System (No. 1610); a UK Biotechnology and Biological Sciences Research Council grant (BBSRC BB/J004308/1). We thank all the reviewers for their valuable comments and suggestions, which are very important for improving this article.

Disclosure statement

No potential conflict of interest was reported by the authors.

Notes

1. There is no obvious choice of metric to estimate the Intercept, and as such we use the default ED metric.

2. As the bandwidth values converge fast and won’t change anymore, only values from the first 50 iterations are drawn in this figure.

Additional information

Funding

Research presented in this paper was jointly supported by projects from the National Natural Science Foundation of China [NSFC: 41401455 and U1533102]; an open research fund of State Key Laboratory of Information Engineering in Surveying, Mapping and Remote Sensing [Grant Number: 14I01]; an open research fund by State Key Laboratory of Resources and Environmental Information System [Grant Number: 1610]; a UK Biotechnology and Biological Sciences Research Council Grant Number: BBSRC BB/J004308/1.