Partitioning a non-symmetric measure of association for three-way contingency tables

Eric Beh (), Biagio Simonetti and Luigi D'Ambra

Journal of Multivariate Analysis, 2007, vol. 98, issue 7, 1391-1411

Abstract: The Goodman-Kruskal tau index is a popular measure of asymmetry for two-way contingency tables where there is a one-way relationship between the variables. Numerous extensions of this index for multi-way tables have been considered in the statistical literature. These include the Gray-Williams measures, Simonetti's delta index and the Marcotorchino index. This paper looks at the partition of the Marcotorchino index for a three-way contingency table with one, two and three ordered categorical variables. Such a partition makes use of orthogonal polynomials and identifies two-way measures of asymmetry (akin to the Goodman-Kruskal tau index) and three-way measures generalisation. These partitions provide information about the structure of the asymmetric relationship between the categories in terms of location, dispersion and higher order moments.

Keywords: Orthogonal polynomials Three-way contingency tables Marcotorchino index Gray-Williams index Location; dispersion and higher order components (search for similar items in EconPapers)
Date: 2007
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Citations: View citations in EconPapers (2)

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