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

Author

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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.

Suggested Citation

  • Beh, Eric J. & Simonetti, Biagio & D'Ambra, Luigi, 2007. "Partitioning a non-symmetric measure of association for three-way contingency tables," Journal of Multivariate Analysis, Elsevier, vol. 98(7), pages 1391-1411, August.
    • Handle: RePEc:eee:jmvana:v:98:y:2007:i:7:p:1391-1411
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    Cited by:

    1. Rosaria Lombardo & Eric J. Beh & Luis Guerrero, 2019. "Analysis of three-way non-symmetrical association of food concepts in cross-cultural marketing," Quality & Quantity: International Journal of Methodology, Springer, vol. 53(5), pages 2323-2337, September.
    2. Pardo, Julio A., 2010. "An approach to multiway contingency tables based on [phi]-divergence test statistics," Journal of Multivariate Analysis, Elsevier, vol. 101(10), pages 2305-2319, November.

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