Multivariate Models of Spatial Dependence

Abstract

Chapter 4 presents several extensions from a univariate context to a multivariate context. These extensions include the replacement of µ1 with Xβ (a trend surface model with autocorrelated errors), a fixed effects multiple linear regression model with autocorrelated errors (for ANOVA), the two-groups discriminant function model with autocorrelated errors, and the bivariate regression model with autocorrelated random variables (a variable effects regression model). This chapter will be concerned with the relationships between spatial autocorrelation and multivariate data sets. One of the first attempts at exploring this issue was reported by Lebart (1969), who assumed the ϱ _j , j = 1, 2, ..., p, autocorrelation parameters for a multivariate data set were the same, and in fact equal to unity. Later, Griffith (1986) outlined a taxonomy of autocorrelation problems for the linear regression model. His discussion alluded to the preoccupation of statisticians either with the case of no autocorrelation in any of these regression model terms, or a concern only with the problem of a spatially autocorrelated error term. In contrast, spatial econometricians have focused much of their attention on an autocorrelated dependent variable.