ABSTRACT
In this chapter, the concern is with spatial variation in the multivariate relations between variables. A range of approaches, including long-established methods and, for example, recent developments in the field of geographically weighted regression (GWR), are reviewed. This chapter has links to Chapter 6, in particular, where the use of regression for prediction purposes is discussed. Global regression is discussed in Section 5.1, while spatial and local regression approaches are the subject of Section 5.2 through Section 5.8. The remaining sections deal with spatially weighted classification and summarise the chapter. The main focus of this chapter is, as would be expected given the
book’s focus, on explicitly local models, but global methods and methods which account for spatial structure, but provide only a single set of output coefficients, are also introduced for context. The techniques discussed allow exploration of variation at different spatial scales. For example, the spatial expansion method enables characterisation of large scale (global) trends, while GWR can be used to fit model parameters over very small scales (limited by the density and number of observations). The common link between the methods outlined in the latter part of this chapter is the ability they offer to account for variation in spatial relations. Several case studies are presented using different methods, and the benefits of applying the selected nonstationary models are considered.
