Interpreting Moran Eigenvector Maps with the Getis-Ord Gi* Statistic

Spatial weights matrices used in quantitative geography furnish maps with their individual latent eigenvectors, whose geographic distributions portray distinct spatial autocorrelation (SA) components. These polygon patterns on maps have specific meaning, partially in terms of geographic scale, which this article describes. The goal of this description is to enable spatial analysts to better understand and interpret these maps individually, as well as mixtures of them, when accounting for SA in a spatial analysis. Linear combinations of Moran eigenvector maps supply a powerful and relatively simple tool that can explain SA in regression residuals, with an ability to render reasonably accurate reproductions of empirical geographic distributions with or without the aid of substantive covariates. The focus of this article is positive SA, the most commonly encountered nature of autocorrelation in georeferenced data. The principal innovative contribution of this article is establishing a better clarification of what the synthetic SA variates extracted from spatial weights matrices epitomize with regard to global, regional, and local clusters of similar values on a map. This article shows that the Getis-Ord Gi* statistic provides a useful tool for classifying Moran eigenvector maps into these three qualitative categories, illustrating findings with a range of specimen geographic landscapes.