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The Effect of Affine Transformation on Redundancy Analysis

Published online by Cambridge University Press:  01 January 2025

Beth K. Dawson-Saunders  and
Maurice M. Tatsuoka
Beth K. Dawson-Saunders*
Affiliation:
Southern Illinois University School of Medicine
Maurice M. Tatsuoka
Affiliation:
University of Illinois at Urbana-Champaign
*
Requests for reprints should be sent to Beth Dawson-Saunders, Department of Medical Humanities, Southern Illinois University School of Medicine, P.O. Box 3926, Springfield, Illinois 62708
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Abstract

Canonical redundancy analysis provides an estimate of the amount of shared variance between two sets of variables and provides an alternative to canonical correlation. The proof that the total redundancy is equal to the average squared multiple correlation coefficient obtained by regressing each variable in the criterion set on all variables in the predictor set is generalized to the case in which there are a larger number of criterion than predictor variables. It is then shown that the redundancy for the criterion set of variables is invariant under affine transformation of the predictor variables, but not invariant under transformation of the criterion variables.

Keywords

canonical correlation
Type
Notes And Comments
Information
Psychometrika , Volume 48 , Issue 2 , June 1983 , pp. 299 - 302
Copyright
Copyright © 1983 The Psychometric Society

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References

Anderson, T. W., An Introduction to Multivariate Statistical Analysis. New York: Wiley, 1958.Google Scholar
Cramer, E. M., & Nicewander, N. A., Some symmetric, invariant measures of multivariate association. Psychometrika, 1979, 44, 43–54.CrossRefGoogle Scholar
Dawson-Saunders, B. K., Correcting for bias in the canonical redundancy statistic. Educational and Psychological Measurement, 1982, 42, 131–143.CrossRefGoogle Scholar
Gleason, T. C., On redundancy in canonical analysis. Psychological Bulletin, 1976, 83, 1004–1006.CrossRefGoogle Scholar
Miller, J. K., In defense of the general canonical correlation index: Reply to Nicewander and Wood. Psychological Bulletin, 1975, 82, 207–209.CrossRefGoogle Scholar
Muller, K. E., Relationships between redundancy analysis, canonical correlation, and multivariate regression. Psychometrika, 1981, 46, 139–142.CrossRefGoogle Scholar
Stewart, D., & Love, W., A general canonical correlation index. Psychological Bulletin, 1968, 70, 160–163.CrossRefGoogle ScholarPubMed
Tatsuoka, M., Multivariate Analysis. New York: Wiley, 1971.Google Scholar
van den Wollenburg, A. L., Redundancy analysis—An alternative for canonical correlation analysis. Psychometrika, 1979, 42, 207–219.CrossRefGoogle Scholar