MESF and multivariate statistical analysis

Abstract

Abstract A fundamental property of multivariate geospatial data is spatial autocorrelation that has common map patterns across attribute variables, which inflates product moment correlations, and patterns unique to individual attribute variables, which deflates product moment correlations. These spatial autocorrelation components impact upon two of the primary features of multivariate statistical analysis, namely, multicollinearity and multiple testing. One outcome is a modification of the orthogonal structure of a set of georeferenced attribute variables, the focus of principal components and factor analyses. Another outcome is the regional differentiation of a geographic landscape by georeferenced attribute variables, the focus of multivariate analysis of variance and discriminant function analysis. A third outcome is the impact on dimensions that span two sets of georeferenced attribute variables, the focus of canonical correlation analysis. A fourth outcome is the alteration of regional clusterings based upon georeferenced attribute variables, the focus of cluster analysis. This chapter demonstrates that spatial autocorrelation matters in multivariate data analysis: decomposing georeferenced data into spatially structured and spatially unstructured components reveals that dimensions uncovered with original attribute data are not necessarily consistent with those uncovered for the pure spatial autocorrelation components (represented by Moran eigenvector spatial filters) or for the aspatial components (represented by eigenvector spatial filter linear regression residuals).