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Relationships between redundancy analysis, canonical correlation, and multivariate regression

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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.

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References

  1. Dawson, B.The sampling distribution of the canonical redundancy statistic. Unpublished doctoral dissertation, University of Illinois, 1977.

  2. Hotelling, H. Relations between two sets of variates.Biometrika, 1936,28, 321–377.

  3. Khatri, C. G. A note on multiple and canonical correlation for a singular covariance matrix.Psychometrika, 1976,41, 465–470.

  4. Stewart, D. & Love, W. A general canonical correlation index.Psychological Bulletin, 1968,70, 160–163.

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

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Author information

Correspondence to Keith E. Muller.

Additional information

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.

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Muller, K.E. Relationships between redundancy analysis, canonical correlation, and multivariate regression. Psychometrika 46, 139–142 (1981) doi:10.1007/BF02293894

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Keywords

  • Linear Regression
  • Public Policy
  • Multiple Linear Regression
  • Statistical Theory
  • Multivariate Regression