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Canonical/Redundancy Factoring Analysis

Published online by Cambridge University Press:  01 January 2025

Wayne S. DeSarbo
Wayne S. DeSarbo*
Affiliation:
Bell Laboratories
*
Requests for reprints should be sent to Wayne S, DeSarbo, Bell Laboratories, Room 2C-479, Murray Hill, N.J. 07974.
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Abstract

The interrelationships between two sets of measurements made on the same subjects can be studied by canonical correlation. Originally developed by Hotelling [1936], the canonical correlation is the maximum correlation between linear functions (canonical factors) of the two sets of variables. An alternative statistic to investigate the interrelationships between two sets of variables is the redundancy measure, developed by Stewart and Love [1968]. Van Den Wollenberg [1977] has developed a method of extracting factors which maximize redundancy, as opposed to canonical correlation.

A component method is presented which maximizes user specified convex combinations of canonical correlation and the two nonsymmetric redundancy measures presented by Stewart and Love. Monte Carlo work comparing canonical correlation analysis, redundancy analysis, and various canonical/redundancy factoring analyses on the Van Den Wollenberg data is presented. An empirical example is also provided.

Keywords

canonical correlationredundancy analysishybrid models
Type
Original Paper
Information
Psychometrika , Volume 46 , Issue 3 , September 1981 , pp. 307 - 329
Copyright
Copyright © 1981 The Psychometric Society

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Footnotes

Wayne S. DeSarbo is a Member of Technical Staff at Bell Laboratories in the Mathematics and Statistics Research Group at Murray Hill, N.J. I wish to express my appreciation to J. Kettenring, J. Kruskal, C. Mallows, and R. Gnanadesikan for their valuable technical assistance and/or for comments on an earlier draft of this paper. I also wish to thank the editor and reviewers of this paper for their insightful remarks.

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