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November 2021 Symmetrical and Non-symmetrical Variants of Three-Way Correspondence Analysis for Ordered Variables
Rosaria Lombardo, Eric J. Beh, Pieter M. Kroonenberg
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Statist. Sci. 36(4): 542-561 (November 2021). DOI: 10.1214/20-STS814


In the framework of multi-way data analysis, this paper presents symmetrical and non-symmetrical variants of three-way correspondence analysis that are suitable when a three-way contingency table is constructed from ordinal variables. In particular, such variables may be modelled using general recurrence formulae to generate orthogonal polynomial vectors instead of singular vectors coming from one of the possible three-way extensions of the singular value decomposition. As we shall see, these polynomials, that until now have been used to decompose two-way contingency tables with ordered variables, also constitute an alternative orthogonal basis for modelling symmetrical, non-symmetrical associations and predictabilities in three-way contingency tables. Consequences with respect to modelling and graphing will be highlighted.


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Rosaria Lombardo. Eric J. Beh. Pieter M. Kroonenberg. "Symmetrical and Non-symmetrical Variants of Three-Way Correspondence Analysis for Ordered Variables." Statist. Sci. 36 (4) 542 - 561, November 2021.


Published: November 2021
First available in Project Euclid: 11 October 2021

MathSciNet: MR4323052
zbMATH: 07473935
Digital Object Identifier: 10.1214/20-STS814

Keywords: ordinal categorical variables , orthogonal polynomials , Symmetrical and non-symmetrical three-way correspondence analysis , trivariate moment decomposition

Rights: Copyright © 2021 Institute of Mathematical Statistics

Vol.36 • No. 4 • November 2021
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