PERMUTATION METHODS FOR DETERMINING THE SIGNIFICANCE OF SPATIAL DEPENDENCE

A class of multivariate nonparametric tests for. spatial dependence, M ultivariate Sequential Permutation Analyses (MSPA), is developed and a pplied to the analysis of spatial data. These rests allow the signific ance level (P value) of the spatial correlation to be computed for eac h lag class. MSPA is shown to be related to the variogram and other me asures of spatial correlation. The interrelationships of these measure s of spatial dependence are discussed and the measures are applied to synthetic and real data. The resulting plot of significance level vs. lag spacing, or P-gram, provides insight into the modeling of the semi variogram and the seminADogram. Although the test clearly rejects some models of correlation, the chief value of the test is to quantify the strength of spatial correlation, and to provide evidence that spatial correlation exists.