Some Properties of Two Measures of Multivariate Association

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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.

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