ABSTRACT
In this chapter, we discuss regression models speci–cally developed for processes described by spatially autocorrelated random variables. The effect of spatial autocorrelation, or apparent spatial autocorrelation, on regression models depends on how these spatial effects in£uence the data (Cliff and Ord, 1981, p. 141). Apparent autocorrelation may or may not be the result of real autocorrelation. Miron (1984) discusses three sources of real or apparent spatial autocorrelation: interaction, reaction, and misspeci–cation. These are not mutually exclusive and may exist in any combination. We will discuss these in the context of a population of plants (for speci–city, let us say they are oak trees in an oak woodland like that of Data Set 2) growing in a particular region. Suppose Yi represents a measure of plant productivity such as tree height or population density at location xi, yi, and that the population is suf–ciently dense relative to the spatial scale that the productivity measure may be modeled as varying continuously with location. For purposes of discussion, suppose that we model tree productivity via a linear regression of the form
Y X Xi i i i= + + +β β β ε0 1 1 2 2 , (13.1)
where Xi1 represents the amount of light available at location i Xi2 represents the amount of available nutrients
In matrix notation, the ordinary least squares (OLS) model is
Y X= +β ε. (13.2)
We will set up models using arti–cial data to demonstrate the various effects of spatial autocorrelation.
