Wednesday, November 28, 2012

Geographically Weighted Regression: A Method for Exploring Spatial Nonstationarity

by Chris Brunsdon, A. Stewart Fotheringham and Martin E. Charlton

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 geogra hically weighted regression, model which allows diferent relationships to exist at diferent 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 investigatin the null non-stationa y one and also for testing whether individual regression coeficients 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 mule unemployment. The paper concludes by discussing ways in which the technique can be extended.

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