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Constrained DEDICOM

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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.

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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.

    Google 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.

    Google 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.

    Google Scholar 

  • Gower, J. C. (1977). The analysis of asymmetry and orthogonality. In J. R. Barra, F. Brodeau, G. Romier, & B. van Cutsem (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.

    Google Scholar 

  • 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.

  • Harshman, R. A. (1981a).Alternating least squares estimation for the single domain DEDICOM model. Unpublished technical memorandum, Bell Laboratories, Murray Hill, NJ.

    Google Scholar 

  • Harshman, R. A. (1981b).DEDICOM Multidimensional analysis of skew-symmetric data. Part I: Theory. Unpublished technical memorandum, Bell Laboratories, Murray Hill, NJ.

    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.

    Google Scholar 

  • Harshman, R. A., & Lundy, M. E. (1990). Multidimensional analysis of preference structures. In A. de Fontenay, M. H. Shugard, & D. S. Sibley (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.

    Google Scholar 

  • Kiers, H. A. L. (in press). An alternating least squares algorithm for PARAFAC2 and DEDICOM3.Computational Statistics and Data Analysis.

  • 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.

    Google Scholar 

  • Penrose, R. (1956). On best approximate solutions of linear matrix equations.Proceedings of the Cambridge Philosophical Society, 52, 17–19.

    Google Scholar 

  • Takane, Y. (1985). Diagonal estimation in DEDICOM.Proceedings of the 1985 annual meeting of the behaviormetric society (pp. 100–101).

  • Takane, Y., Kiers, H. A. L., & de Leeuw, J. (1991).Components analysis with different sets of constraints on different dimensions. Manuscript submitted for publication.

  • Takane, Y., & Shibayama, T. (1991). Principal component analysis with external information on both subjects and variables.Psychometrika, 56, 97–120.

    Google 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.

    Google Scholar 

  • ten Berge, J. M. F., & Nevels, K. (1977). A general solution to Mosier's oblique Procrustes problem.Psychometrika, 42, 593–600.

    Google 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 (Rhodeus amarus Bloch).Archives Neerlandaises de Zoologie, 14, 103–199.

    Google Scholar 

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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.

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Kiers, H.A.L., Takane, Y. Constrained DEDICOM. Psychometrika 58, 339–355 (1993). https://doi.org/10.1007/BF02294580

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  • DOI: https://doi.org/10.1007/BF02294580

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