Moran's I for Multivariate Spatial Data.

Moran's I is a spatial autocorrelation measure of univariate spatial data. Therefore, even if p spatial data exist, we can only obtain p values for Moran's I. In other words, Moran's I cannot measure the degree of spatial autocorrelation of multivariate spatial data as a single value. This paper addresses this issue. That is, we extend Moran's I so that it can measure the degree of spatial autocorrelation of multivariate spatial data as a single value. In addition, since the local version of Moran's I has the same problem, we extend it as well. Then, we establish their properties, which are fundamental for applied work. Numerical illustrations of the theoretical results obtained in the paper are also provided. [ABSTRACT FROM AUTHOR]