Detecting negative spatial autocorrelation in georeferenced random variables

Negative spatial autocorrelation refers to a geographic distribution of values, or a map pattern, in which the neighbors of locations with large values have small values, the neighbors of locations with intermediate values have intermediate values, and the neighbors of locations with small values have large values. Little is known about negative spatial autocorrelation and its consequences in statistical inference in general, and regression-based inference in particular, with spatial researchers to date concentrating mostly on understanding the much more frequently encountered case of positive spatial autocorrelation. What are the spatial contexts within which negative spatial autocorrelation should be readily found? What are its inferential consequences for regression models? This paper presents selected empirical examples of negative spatial autocorrelation, adding to the slowly growing literature about this phenomenon.