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Psychometrika

, Volume 53, Issue 4, pp 487–494 | Cite as

Generalized approaches to the maxbet problem and the maxdiff problem, with applications to canonical correlations

  • Jos M. F. ten Berge
Article

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.

Key words

matching configurations Procrustes rotation SUMCOR MAXCOR successive blocks 

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References

  1. Burt, C. (1948). The factorial study of temperamental traits.British Journal of Psychology, Statistical Section, 1, 178–203.Google Scholar
  2. Cliff, N., & Krus, D. J. (1976). Interpretation of canonical analysis: Rotated vs. unrotated solutions.Psychometrika, 41, 35–42.Google Scholar
  3. Horst, P. (1961). Relations amongm sets of measures.Psychometrika, 26, 129–149.Google Scholar
  4. Horst, P. (1965).Factor analysis of data matrices. New-York: Holt.Google Scholar
  5. Hotelling, H. (1933). Analysis of a complex of statistical variables into principal components.Journal of Educational Psychology, 24, 417–441; 498–520.Google Scholar
  6. Kettenring, J. R. (1971). Canonical analysis of several sets of variables.Biometrika, 58, 433–451.Google Scholar
  7. Kristof, W., & Wingersky, B. (1971). Generalization of the orthogonal Procrustes rotation procedure for more than two matrices.Proceedings of the 79th Annual convention of the American Psychological Association, 6, 89–90.Google Scholar
  8. Lingoes, J. C., & Borg, I. (1978). A direct approach to individual differences scaling using increasingly complex transformations.Psychometrika, 43, 491–519.Google Scholar
  9. Reynolds, T. J., & Jackosfsky, E. F. (1981). Interpreting canonical analysis: The use of orthogonal transformations.Educational and Psychological Measurement, 41, 661–671.Google Scholar
  10. Rutishauser, H. (1969). Computational aspects of F. L. Bauer's simultaneous iteration method.Numerische Mathematik, 13, 4–13.Google Scholar
  11. ten Berge, J. M. F. (1977). Orthogonal Procrustes rotation for two or more matrices.Psychometrika, 42, 267–276.Google Scholar
  12. ten Berge, J. M. F. (1986). A general solution for the Maxbet problem. In J. de Leeuw, W. J. Heiser, J. Meulman, & F. Critchley (Eds.),Multidimensional data analysis (pp. 81–87). Leiden: DSWO-press.Google Scholar
  13. ten Berge, J. M. F. & Knol, D. L. (1984). Orthogonal rotations to maximal agreement for two or more matrices of different column orders.Psychometrika, 49, 49–55.Google Scholar
  14. Tucker, L. R. (1951).A method for synthesis of factor analysis studies. (Personnel Research Section Report N. 984). Washington, D.C.: Department of the Army.Google Scholar
  15. van de Geer, J. P. (1984). Linear relations amongk sets of variables.Psychometrika, 49, 70–94.Google Scholar

Copyright information

© The Psychometric Society 1988

Authors and Affiliations

  • Jos M. F. ten Berge
    • 1
  1. 1.University of GroningenThe Netherlands

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