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Constrained DEDICOM

Published online by Cambridge University Press:  01 January 2025

Henk A. L. Kiers  and
Yoshio Takane
Henk A. L. Kiers*
Affiliation:
University of Groningen
Yoshio Takane
Affiliation:
McGill University
*
Requests for reprints should be sent to Henk A. L. Kiers, Department of Psychology (PIOP), Grote Kruisstr. 2/1, 9712 TS Groningen, THE NETHERLANDS.
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Abstract

The DEDICOM method for the analysis of asymmetric data tables gives representations that are identified only up to a nonsingular transformation. To identify solutions it is proposed to impose subspace constraints on the stimulus coefficients. Most attention is paid to the case where different subspace constraints are imposed on different dimensions. The procedures are discussed both for the case where the complete table is fitted, and for cases where only offdiagonal elements are fitted. The case where the data table is skew-symmetric is treated separately as well.

Keywords

asymmetric relationshipsalternating least squares
Type
Original Paper
Information
Psychometrika , Volume 58 , Issue 2 , June 1993 , pp. 339 - 355
Copyright
Copyright © 1993 The Psychometric Society

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Footnotes

The research of H. A. L. Kiers has been made possible by a fellowship of the Royal Netherlands Academy of Arts and Sciences. The research of Y. Takane has been supported by the Natural Sciences and Engineering Research Council of Canada, grant number A6394, and by the McGill-IBM Cooperative Grant. The authors are obliged to Richard A. Harshman for helpful comments on an earlier version.

References

Carroll, J. D., Pruzansky, S., Kruskal, J. B. (1980). CANDELINC: A general approach to multidimensional analysis of many-way arrays with linear constraints on parameters. Psychometrika, 45, 3–24.CrossRefGoogle Scholar
Chino, N. (1991). A critical review of the analysis of asymmetric relational data. Bulletin of the Faculty of Letters of Aichi Gakuin University, 21, 31–52.Google Scholar
Constantine, A. G., Gower, J. C. (1978). Graphical representations of asymmetric matrices. Applied Statistics, 27, 297–304.CrossRefGoogle Scholar
Dawson, M. R. W., Harshman, R. A. (1986). The multidimensional analysis of asymmetries in alphabetic confusion matrices: Evidence for global-to-local and local-to-global processing. Perception & Psychophysics, 40, 370–383.CrossRefGoogle ScholarPubMed
Gower, J. C. (1977). The analysis of asymmetry and orthogonality. In Barra, J. R., Brodeau, F., Romier, G., van Cutsem, B. (Eds.), Recent developments in statistics (pp. 109–123). Amsterdam: North-Holland Publishing Company.Google Scholar
Harman, H. H., Jones, W. H. (1966). Factor analysis by minimizing residuals (Minres). Psychometrika, 31, 351–368.CrossRefGoogle ScholarPubMed
Harshman, R. A. (1978, August). Models for analysis of asymmetrical relationships among N objects or stimuli. Paper presented at the First Joint Meeting of the Psychometric Society and the Society for Mathematical Psychology, Hamilton, Ontario.Google Scholar
Harshman, R. A. (1981). Alternating least squares estimation for the single domain DEDICOM model, Murray Hill, NJ: Bell Laboratories.Google Scholar
Harshman, R. A. (1981). DEDICOM Multidimensional analysis of skew-symmetric data. Part I: Theory, Murray Hill, NJ: Bell Laboratories.Google Scholar
Harshman, R. A., Green, P. E., Wind, Y., Lundy, M. E. (1982). A model for the analysis of asymmetric data in marketing research. Marketing Science, 1, 205–242.CrossRefGoogle Scholar
Harshman, R. A., Lundy, M. E. (1990). Multidimensional analysis of preference structures. In de Fontenay, A., Shugard, M. H., Sibley, D. S. (Eds.), Telecommunications demand modelling: An integrated view (pp. 185–204). Amsterdam: Elsevier Science Publishers B.V..Google Scholar
Kiers, H. A. L. (1989). An alternating least squares algorithm for fitting the two- and three-way DEDICOM model and the IDIOSCAL model. Psychometrika, 54, 515–521.CrossRefGoogle Scholar
Kiers, H. A. L. (in press). An alternating least squares algorithm for PARAFAC2 and DEDICOM3. Computational Statistics and Data Analysis.Google Scholar
Kiers, H. A. L., ten Berge, J. M. F., Takane, Y., de Leeuw, J. (1990). A generalization of Takane's algorithm for DEDICOM. Psychometrika, 55, 151–158.CrossRefGoogle Scholar
Penrose, R. (1956). On best approximate solutions of linear matrix equations. Proceedings of the Cambridge Philosophical Society, 52, 17–19.CrossRefGoogle Scholar
Takane, Y. (1985). Diagonal estimation in DEDICOM. Proceedings of the 1985 annual meeting of the behaviormetric society (pp. 100–101).Google Scholar
Takane, Y., Kiers, H. A. L., & de Leeuw, J. (1991). Components analysis with different sets of constraints on different dimensions. Manuscript submitted for publication.Google Scholar
Takane, Y., Shibayama, T. (1991). Principal component analysis with external information on both subjects and variables. Psychometrika, 56, 97–120.CrossRefGoogle Scholar
ten Berge, J. M. F., Kiers, H. A. L. (1989). Fitting the off-diagonal DEDICOM model in the least-squares sense by a generalization of the Harman & Jones MINRES procedure of factor analysis. Psychometrika, 54, 333–337.CrossRefGoogle Scholar
ten Berge, J. M. F., Nevels, K. (1977). A general solution to Mosier's oblique Procrustes problem. Psychometrika, 42, 593–600.CrossRefGoogle Scholar
van der Heijden, P. G. M. (1987). Correspondence analysis of longitudinal categorical data, Leiden: DSWO Press.Google Scholar
Wiepkema, P. R. (1961). An ethological analysis of the reproductive behaviour of the bitterling. Archives Neerlandaises de Zoologie, 14, 103–199.CrossRefGoogle Scholar