Dr. Chris Brunsdon is lecturer in computer-based methods in the Department of Town and Country Planning, A. Stewart Fotheringham is Professor of Quantitative Geography, and Martin Charlton is lecturer in GIS in the Department of Geography, all at Newcastle University.
Geographically Weighted Regression: A Method for Exploring Spatial Nonstationarity
Article first published online: 3 SEP 2010
1996 The Ohio State University
Volume 28, Issue 4, pages 281–298, October 1996
How to Cite
Brunsdon, C., Fotheringham, A. S. and Charlton, M. E. (1996), Geographically Weighted Regression: A Method for Exploring Spatial Nonstationarity. Geographical Analysis, 28: 281–298. doi: 10.1111/j.1538-4632.1996.tb00936.x
- Issue published online: 3 SEP 2010
- Article first published online: 3 SEP 2010
- Revised version accepted 2/16/96
Spatial nonstationarity is a condition in which a simple “global” model cannot explain the relationships between some sets of variables. The nature of the model must alter over space to reflect the structure within the data. In this paper, a technique is developed, termed geographically weighted regression, which attempts to capture this variation by calibrating a multiple regression model which allows different relationships to exist at different points in space. This technique is loosely based on kernel regression. The method itself is introduced and related issues such as the choice of a spatial weighting function are discussed. Following this, a series of related statistical tests are considered which can be described generally as tests for spatial nonstationarity. Using Monte Carlo methods, techniques are proposed for investigating the null hypothesis that the data may be described by a global model rather than a non-stationary one and also for testing whether individual regression coefficients are stable over geographic space. These techniques are demonstrated on a data set from the 1991 U.K. census relating car ownership rates to social class and male unemployment. The paper concludes by discussing ways in which the technique can be extended.