Abstract
The objective of this paper is to introduce and motivate additional properties and interpretations for the redundancy variables. It is shown that these variables can be derived by application of certain invariance arguments and without reference to the index of redundancy. In addition, an optimality property for the variables is presented which is important whenever one restricts attention in a study to a subset of the redundancy variables. This optimality property pertains to the subset rather than to the individual variables.
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Cramer, E. M. & Nicewander, W. A. Some symmetric, invariant measures of multivariate association.Psychometrika, 1979,44, 43–54.
Gleason, T. C. On redundancy in canonical analysis.Psychological Bulletin, 1976, 83, 1004–1006.
Izenman, A. J. Reduced-rank regression for the multivariate linear model.Journal of Multivariate Analysis, 1976,5, 248–264.
Johansson, J. K. An extension of Wollenberg's redundancy analysis.Psychometrika, 1981,46, 93–103.
Miller, J. K. & Farr, S. D. Bi-multivariate redundancy: a comprehensive measure of interbattery relationship.Multivariate Behavior Research, 1971,6, 313–324.
Nicewander, W. A. & Wood, D. A. Comments on “A general canonical correlation index.”Psychological Bulletin, 1974,81, 92–94.
Nicewander, W. A. & Wood, D. A. On the mathematical bases of the general canonical correlation index: rejoinder to Miller.Psychological Bulletin, 1975,82, 210–212.
Okamoto, M. Optimality of principal components. In P. R. Krishnaiah (ed.),Multivariate Analysis II. New York: Academic Press, 1969, pp. 673–685.
Rao, C. R. The use and interpretation of principal components analysis in applied research.Sankhya A, 1964,26, 329–358.
Stewart, D. and Love, W. A general canonical correlation index.Psychological Bulletin, 1968,70, 160–163.
Timm, N. H.Multivariate Analysis with Applications in Education and Psychology. Monterey, California: Brooks/Cole Publishing Company, 1975.
Tyler, D. E. A counterexample to Miller and Farr's algorithm for the index of redundancy. To appear,Multivariate Behavior Research, 1982.
van den Wollenberg, A. L. Redundancy analysis: an alternative to canonical correlation analysis.Psychometrika, 1977,42, 207–219.
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This paper is based in part on the author's doctoral dissertation, Department of Statistics, Princeton, University. Research was conducted under the supervision of Lawrence S. Mayer.
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Tyler, D.E. On the optimality of the simultaneous redundancy transformations. Psychometrika 47, 77–86 (1982). https://doi.org/10.1007/BF02293852
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DOI: https://doi.org/10.1007/BF02293852