Two techniques for exploring non-stationarity in geographical data

This paper is concerned with the exploratory analysis of non-stationarity, the variation in parameter estimates across data sets, in spatial data. Two modelling paradigms are demonstrated in which local variation in the structure of a model is considered rather than the fitting of a global model to a set of spatial data. Using data for an area in North East Scotland, we first demonstrate some problems of non-stationarity in a multiple regression model using a moving window to fit a large number of local models within the study area, the results of the modelling being visualised in a GIS environment. In particular we examine the localised variation in the model coefficients and goodness of fit. The second technique consists of a more formal modelling framework in which spatial non-stationarity can be both measured and modelled. This technique is known as Geographically Weighted Regression (GWR) and an empirical example of the technique is described using data on the relationship between health and socio-economic data in the city of Newcastle in Northeast England.