The General Linear Model and Spatial Autoregressive Models

Abstract

Specific instances of the general linear model (GLM) have already been implemented within spatial statistics. Griffith (1978) summarizes how to write the simple one- way ANOVA model in the presence of spatial autocorrelation, more recently extending this to N-way ANOVA and unbalanced designs [Griffith (1992b)]. This recent article highlights the need for more work on mixed and random effects unbalanced design models, which is the case in traditional statistics as well. Griffith (1979) describes how to write the one-way MANOVA model for geo-referenced data, more recently extending this to N-way MANOVA and unbalanced designs [Griffith (1992b)], too. His initial findings in this case are consistent with the perspective promoted by Haining (1991). Griffith (1989) has also outlined spatial Statistical two-groups discriminant function analysis and ANCO VA models [see also Anselin (1988), for a spatial econometric implementation of this latter model]. Other attempts along these lines are found in Switzer (1985), who has devised a spatial principal components analysis, Mardia (1988) and Griffith (1988), who have constructed multivariate geo-referenced data models, and Wartenberg (1985), who has formulated a cross-Moran Coefficient (cross-MC). And, Cressie and Hilterbrand (1993) have studied the problem of multivariate geo-statistics. What remains explicitly unaddressed is treatment of canonical correlation, and a spatial Statistical fc-groups discriminant function analysis model (which should relate to the eigenvectors of the aforementioned spatially adjusted MANOVA model).