Some symmetric,invariant measures of multivariate association |
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Authors: | Elliot M Cramer W Alan Nicewander |
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Institution: | (1) The L. L. Thurstone Psychometric Laboratory, Davie Hall, The University of North Carolina at Chapel Hill, 27514 Chapel Hill, NC;(2) University of Oklahoma, USA |
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Abstract: | A distinction is drawn between redundancy measurement and the measurement of multivariate association for two sets of variables. Several measures of multivariate association between two sets of variables are examined. It is shown that all of these measures are generalizations of the (univariate) squared-multiple correlation; all are functions of the canonical correlations, and all are invariant under linear transformations of the original sets of variables. It is further shown that the measures can be considered to be symmetric and are strictly ordered for any two sets of observed variables. It is suggested that measures of multivariate relationship may be used to generalize the concept of test reliability to the case of vector random variables. |
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Keywords: | canonical correlation multivariate analysis association redundancy |
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