Categorical Wombling: Detecting Regions of Significant Change in Spatially Located Categorical Variables

Wombling is a method for discovering boundaries in a collection of continuous variables observed at the same geographic localities. We extend this method to categorical data. A categorical wombling statistic C_i, which identifies areas of rapid change, is defined for every pair i = 1,…, n of adjacent localities, and is equal to the average number of category mismatches at i. We use both simulation and theory to consider the order statistics of C_i under null hypotheses of randomness, and of spatial autocorrelation for each variable, but independence between variables. Graph-theoretical statistics derived from C_i investigate whether areas of rapid change resemble boundaries. Computer simulation is used to study the distributions of these under the two null hypotheses. The methods are applied to linguistic data in three European areas. Other potential applications exist in biology, linguistics, anthropology, and other social sciences.