Modelling Area Data
Exploratory spatial data analysis is often a preliminary step to more formal modelling approaches that seek to establish relationships between the observations of a variable and the observations of other variables, recorded for each areal unit. The focus in this chapter is on spatial regression models in a simple cross-sectional setting, leaving out of consideration the analysis of panel data. We, moreover, assume that the data concerned can be taken to be approximately normally distributed. This assumption is—to varying degrees—involved in most of the spatial regression techniques that we will consider. Note that the assumption of normality is not tenable if the variable of interest is a count or a proportion. In these cases we would expect models for such data to involve probability distributions such as the Poisson or binomial. The chapter consists of five sections, starting with a treatment of the specification of spatial dependence in a regression model. Next, specification tests are considered to detect the presence of spatial dependence. This is followed by a review of the spatial Durbin model (SDM) that nests many of the models widely used in the literature, and by a discussion of spatial regression model estimation based on the maximum likelihood (ML) principle. The chapter closes with some remarks on model parameter interpretation, an issue that had been largely neglected so far. Readers interested in implementing the models, methods and techniques discussed in this chapter find useful MATLAB code which is publicly available at spatial-econometrics.com, LeSage’s spatial econometrics toolbox (downloadable from http://www.spatial-econometrics.com/), see Liu and LeSage (2010) Journal of Geographical Systems 12(1):69–87 for a brief description. Another useful open software is the spdep package of the R project (downloadable from http://cran.r-project.org).