A generalized significance testing method for global measures of spatial association: an extension of the Mantel test

This research is concerned with providing a generalized significance testing method for global measures of spatial association by extending the Mantel test. Even though it has long been recognized that univariate spatial association measures such as Moran's <i>I </i>and Geary's <i>c </i>are special cases of Mantel's generalized association statistic, an intensive and comprehensive examination of the connections, particularly in terms of significance testing has never been undertaken. Furthermore, researchers have faced difficulties in dealing with spatial weights matrices with <i>nonzero </i>diagonal elements, and establishing the significance testing method for <i>bivariate </i>spatial association measures such as Cross - Moran and Lee's <i>L </i>. The author demonstrates that the proposed extended Mantel test can be applied to any global measure of spatial association with any form of spatial weights matrix in order to approximate the first two moments of the measures. A Monte Carlo simulation for each measure with various forms of spatial weights matrices confirms the exactness of the approximation.