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Generalized Approaches to the Maxbet Problem and the Maxdiff Problem, with Applications to Canonical Correlations

Published online by Cambridge University Press:  01 January 2025

Jos M. F. ten Berge
Jos M. F. ten Berge*
Affiliation:
University of Groningen
*
Requests for reprints should be sent to Jos M.F. ten Berge, Vakgroep Psychologic, RU Groningen, Grote Markt 32, 9712 HV Groningen, THE NETHERLANDS.
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Abstract

Van de Geer has reviewed various criteria for transforming two or more matrices to maximal agreement, subject to orthogonality constraints. The criteria have applications in the context of matching factor or configuration matrices and in the context of canonical correlation analysis for two or more matrices. The present paper summarizes and gives a unified treatment of fully general computational solutions for two of these criteria, Maxbet and Maxdiff. These solutions will be shown to encompass various well-known methods as special cases. It will be argued that the Maxdiff solution should be preferred to the Maxbet solution whenever the two criteria coincide. Horst's Maxcor method will be shown to lack the property of monotone convergence. Finally, simultaneous and successive versions of the Maxbet and Maxdiff solutions will be treated as special cases of a fully flexible approach where the columns of the rotation matrices are obtained in successive blocks.

Keywords

matching configurationsProcrustes rotationSUMCORMAXCORsuccessiveblocks
Type
Original Paper
Information
Psychometrika , Volume 53 , Issue 4 , December 1988 , pp. 487 - 494
Copyright
Copyright © 1988 The Psychometric Society

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Footnotes

The author is obliged to Henk Kiers for computational assistance and helpful comments.

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