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Categorical Wombling: Detecting Regions of Significant Change in Spatially Located Categorical Variables
Author(s) -
Oden Neal L.,
Sokal Robert R.,
Fortin MarieJosée,
Goebl Hans
Publication year - 1993
Publication title -
geographical analysis
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.773
H-Index - 65
eISSN - 1538-4632
pISSN - 0016-7363
DOI - 10.1111/j.1538-4632.1993.tb00301.x
Subject(s) - categorical variable , statistic , randomness , statistics , spatial analysis , null hypothesis , null model , mathematics
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.