Geographically weighted regression with a non-Euclidean distance metric: a case study using hedonic house price data

Abstract

Geographically weighted regression (GWR) is an important local technique for exploring spatial heterogeneity in data relationships. In fitting with Tobler’s first law of geography, each local regression of GWR is estimated with data whose influence decays with distance, distances that are commonly defined as straight line or Euclidean. However, the complexity of our real world ensures that the scope of possible distance metrics is far larger than the traditional Euclidean choice. Thus in this article, the GWR model is investigated by applying it with alternative, non-Euclidean distance (non-ED) metrics. Here we use as a case study, a London house price data set coupled with hedonic independent variables, where GWR models are calibrated with Euclidean distance (ED), road network distance and travel time metrics. The results indicate that GWR calibrated with a non-Euclidean metric can not only improve model fit, but also provide additional and useful insights into the nature of varying relationships within the house price data set.

Keywords:

• local regression
• non-stationarity
• road network distance
• travel time
• real estate

Acknowledgements

The research presented in this article was funded by a Strategic Research Cluster grant (07/SRC/I1168) by the Science Foundation Ireland under the National Development Plan. We thank all the reviewers for their valuable comments and suggestions, which are very important for improving this article.

Notes

^1. This may be due to a certain ignorance of its importance or more likely due to a lack of suitable software. In the latter case, this is somewhat addressed with the GWmodel R package.

^2. Future research could investigate this source of uncertainty more closely, together with its impact on model outputs. Simulation studies may help in this respect.

^3. The idea of transforming the coordinate system can also be found in the context of non-stationary spatial covariance estimation. For example, see the coastal water distance study of Løland and Høst (2003) where non-ED metrics are required and the related deformation methods of Sampson and Guttorp (1992).