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Multidimensional Scaling with Different Orientations of Dimensions for Symmetric and Asymmetric Relationships

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Summary

A model and an associated nonmetric algorithm for analyzing two-mode three-way asymmetric proximities are presented. The model represents proximity relationships among objects which are common to all sources, the salience of symmetric proximity relationships along dimensions for each source, and the salience of asymmetric proximity relationships along dimensions. The salience of asymmetric proximity relationships is represented by a set of dimensions, which have different orientations from that for the symmetric relationships.

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References

  • Carroll, J. D. and Chang. J. J. (1970). Analysis of individual differences in multidimensional scaling via an N-way generalization of ‘Eckart-Young’ decomposition. Psychometrika, 35, 283–319.

    Article  MATH  Google Scholar 

  • Chino, N., Grorud, A., and Yoshino, R. (1996). A complex analysis for two-mode three-way asymmetric relational data. Proc. of the 5th Conference of the International Federation of Classification Societies at Kobe, Japan (vol. 2 ), 83–86.

    Google Scholar 

  • DeSarbo, W. S., Johnson, M. D., Manrai, A. K., Manrai, L. A., and Edwards, E. A. (1992). TSCALE: A new multidimensional scaling procedure based on Tversky’s contrast model. Psychometrika, 57, 43–69.

    Article  MATH  Google Scholar 

  • Kruskal, J. B. and Carroll, J. D. (1969). Geometric models and badness-of-fit measures. In Multivariate Analysis, Krishnaiah, P. K. (ed.), 639–671. Academic Press, New York.

    Google Scholar 

  • Okada, A. and Imaizumi, T. (1997). Asymmetric multidimensional scaling of two-mode three-way proximities. Journal of Classification, 14, 195–224.

    Article  MATH  Google Scholar 

  • Okada, A. and Imaizumi, T. (2000a). A generalization of two-mode three-way asymmetric multidimensional scaling. Proc. of the 24th Annual Conference of the German Classification Society, 115.

    Google Scholar 

  • Okada, A. and Imaizumi, T. (2000b). Multidimensional scaling with different orientations of symmetric and asymmetric dimensions. Proc. of the International Conference on Measurement and Multivariate Analysis at Banff, Canada (vol. 1 ), 124–126.

    Google Scholar 

  • Okada, A. and Imaizumi, T. (2000c). Two-mode three-way asymmetric multidimensional scaling with constraints on asymmetry. In Classification and Information Processing at the Turn of the Millennium, Decker, R. et al. (eds.), 52–59. Springer-Verlag, Berlin.

    Book  Google Scholar 

  • Zielman, B. (1991). Three-way scaling of asymmetric proximities. Research Report RR91–01, Department of Data Theory, University of Leiden, Leiden.

    Google Scholar 

  • Zielman, B. and Heiser, W. J. (1993). Analysis of asymmetry by a slide-vector. Psychometrika, 58, 101–114.

    Article  MATH  Google Scholar 

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© 2002 Springer Japan

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Okada, A., Imaizumi, T. (2002). Multidimensional Scaling with Different Orientations of Dimensions for Symmetric and Asymmetric Relationships. In: Nishisato, S., Baba, Y., Bozdogan, H., Kanefuji, K. (eds) Measurement and Multivariate Analysis. Springer, Tokyo. https://doi.org/10.1007/978-4-431-65955-6_10

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  • DOI: https://doi.org/10.1007/978-4-431-65955-6_10

  • Publisher Name: Springer, Tokyo

  • Print ISBN: 978-4-431-65957-0

  • Online ISBN: 978-4-431-65955-6

  • eBook Packages: Springer Book Archive

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