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Interpreting Canonical Correlation Analysis through Biplots of Structure Correlations and Weights

Published online by Cambridge University Press:  01 January 2025

Cajo J. F. ter Braak
Cajo J. F. ter Braak*
Affiliation:
Agricultural Mathematics Group, Research Institute for Nature Management
*
Requests for reprints should be sent to Cajo J. F. ter Braak, Agricultural Mathematics Group, Box 100, 6700 AC Wageningen, THE NETHERLANDS.
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Abstract

This paper extends the biplot technique to canonical correlation analysis and redundancy analysis. The plot of structure correlations is shown to the optimal for displaying the pairwise correlations between the variables of the one set and those of the second. The link between multivariate regression and canonical correlation analysis/redundancy analysis is exploited for producing an optimal biplot that displays a matrix of regression coefficients. This plot can be made from the canonical weights of the predictors and the structure correlations of the criterion variables. An example is used to show how the proposed biplots may be interpreted.

Keywords

biplotcanonical correlation analysiscanonical weightinterbattery factor analysispartial analysisredundancy analysisregression coefficientreduced rank regressionstructure correlations
Type
Original Paper
Information
Psychometrika , Volume 55 , Issue 3 , September 1990 , pp. 519 - 531
Copyright
Copyright © 1990 The Psychometric Society

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Footnotes

I am indebted to L. C. A. Corsten, K. R. Gabriel, A. Z. Israëls, J. M. F. ten Berge, H. A. L. Kiers, J. de Bree and A. A. M. Jansen for comments on the manuscript.

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