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Some Properties of Two Measures of Multivariate Association

Published online by Cambridge University Press:  01 January 2025

Willem van den Burg  and
Charles Lewis
Willem van den Burg*
Affiliation:
University of Groningen
Charles Lewis
Affiliation:
Educational Testing Service
*
Requests for reprints should be sent to Willem van den Burg, Department of Neuropsychology, Neurological Clinic, Oostersingel 59, 9713 EZ Groningen, THE NETHERLANDS.
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Abstract

Two kinds of measures of multivariate association, based on Wilks' Λ and the Bartlett-Nanda-Pillai trace criterion V, respectively, are compared in terms of properties of the univariate R2 which they generalize. A unified set of derivations of the properties is provided which are self-contained and not restricted to decompositions in canonical variates. One conclusion is that a symmetric index based on Λ allows generalization of the multiplicative decomposition of R2 in terms of squared partial correlations, but not the additive decomposition in terms of squared semipartial correlations, while the reverse is true for an asymmetric index based on V.

Keywords

set correlationWilks' Λtrace criterionpredictabilityredundancy index
Type
Original Paper
Information
Psychometrika , Volume 53 , Issue 1 , March 1988 , pp. 109 - 122
Copyright
Copyright © 1988 The Psychometric Society

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Footnotes

We are indebted to Jos M. F. ten Berge for some fruitful discussions.

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