The Minkowski approach for choosing the distance metric in geographically weighted regression

ABSTRACT

In this study, the geographically weighted regression (GWR) model is adapted to benefit from a broad range of distance metrics, where it is demonstrated that a well-chosen distance metric can improve model performance. How to choose or define such a distance metric is key, and in this respect, a ‘Minkowski approach’ is proposed that enables the selection of an optimum distance metric for a given GWR model. This approach is evaluated within a simulation experiment consisting of three scenarios. The results are twofold: (1) a well-chosen distance metric can significantly improve the predictive accuracy of a GWR model; and (2) the approach allows a good approximation of the underlying ‘optimal distance metric’, which is considered useful when the ‘true’ distance metric is unknown.

Keywords:

• Non-stationarity
• GW model
• Minkowski distance
• simulation experiment

ORCID

Chris Brunsdon http://orcid.org/0000-0003-4254-1780

Notes

^1. The period of Equation (5) is , that is, very close to 1.57, so a rotation of 1.57 will be almost no different from a 0 rotation.

^2. Coordinate rotations are invalid for ED, so the model is only calibrated once, when p is 2.

Additional information

Funding

Research presented in this paper was supported by projects from the National Natural Science Foundation of China [NSFC: 41401455], [NSFC: 41331175]; a Strategic Research Cluster [grant number 07/SRC/I1168] by the Science Foundation Ireland under the National Development Plan; and the North Wyke Farm Platform supported by the Biotechnology and Biological Sciences Research Council of the UK [BBSRC BB/J004308].