Modelling Areal Data

We have seen in Chap. 9 that the lack of independence between observations in spatial data — spatial autocorrelation — is commonplace, and that tests are available. In an ideal world, one would prefer to gather data in which the observations were mutually independent, and so avoid problems in inference from analytical results. Most applied data analysts, however, do not have this option, and must work with the data that are available, or that can be collected with available technologies. It is quite often the case that observations on relevant covariates are not available at all, and that the detection of spatial autocorrelation in data or model residuals in fact constitutes the only way left to model the remaining variation.

In this chapter, we show how spatial structure in dependence between observations may be modelled, in particular for areal data, but where necessary also using alternative representations. We look at spatial econometrics approaches separately, because the terminology used in that domain differs somewhat from other areas of spatial statistics. We cover spatial filtering using Moran eigenvectors and geographically weighted regression in this chapter, but leave Bayesian hierarchical models until Chap. 11.