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Relationships between Redundancy Analysis, Canonical Correlation, and Multivariate Regression

Published online by Cambridge University Press:  01 January 2025

Keith E. Muller
Keith E. Muller*
Affiliation:
University of North Carolina
*
Requests for reprints should be sent to Keith E. Muller, Department of Biostatistics, Rosenau Hall 201H, University of North Carolina, Chapel Hill, North Carolina, 27514.
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Abstract

This paper attempts to clarify the nature of redundancy analysis and its relationships to canonical correlation and multivariate multiple linear regression. Stewart and Love introduced redundancy analysis to provide non-symmetric measures of the dependence of one set of variables on the other, as channeled through the canonical variates. Van den Wollenberg derived sets of variates which directly maximize the between set redundancy. Multivariate multiple linear regression on component scores (such as principal components) is considered. The problem is extended to include an orthogonal rotation of the components. The solution is shown to be identical to van den Wollenberg's maximum redundancy solution.

Type
Original Paper
Information
Psychometrika , Volume 46 , Issue 2 , June 1981 , pp. 139 - 142
Copyright
Copyright © 1981 The Psychometric Society

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Footnotes

This research was supported in part by U.S. Environmental Protection Agency contract 68-02-3402. The author gratefully acknowledges the stimulation of Maurice Tatsuoka and Beth Dawson-Saunders in first interesting him in redundancy analysis, as well as a useful change suggested by Warren Sarle.

References

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van den Wollenberg, A. L. Redundancy analysis, an alternative for canonical correlation analysis. Psychometrika, 1977, 42, 207–219.CrossRefGoogle Scholar