Relationships between redundancy analysis, canonical correlation, and multivariate regression
- 277 Downloads
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.
KeywordsLinear Regression Public Policy Multiple Linear Regression Statistical Theory Multivariate Regression
Unable to display preview. Download preview PDF.
- Dawson, B.The sampling distribution of the canonical redundancy statistic. Unpublished doctoral dissertation, University of Illinois, 1977.Google Scholar
- Hotelling, H. Relations between two sets of variates.Biometrika, 1936,28, 321–377.Google Scholar
- Khatri, C. G. A note on multiple and canonical correlation for a singular covariance matrix.Psychometrika, 1976,41, 465–470.Google Scholar
- Stewart, D. & Love, W. A general canonical correlation index.Psychological Bulletin, 1968,70, 160–163.Google Scholar
- van den Wollenberg, A. L. Redundancy analysis, an alternative for canonical correlation analysis.Psychometrika, 1977,42, 207–219.Google Scholar