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

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  • Beh, Eric J.
  • Simonetti, Biagio
  • D'Ambra, Luigi

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.

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Bibliographic Info

Article provided by Elsevier in its journal Journal of Multivariate Analysis.

Volume (Year): 98 (2007)
Issue (Month): 7 (August)
Pages: 1391-1411

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Handle: RePEc:eee:jmvana:v:98:y:2007:i:7:p:1391-1411

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Keywords: Orthogonal polynomials Three-way contingency tables Marcotorchino index Gray-Williams index Location; dispersion and higher order components;

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