Advertisement

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

  • Akinori Okada
  • Tadashi Imaizumi

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.

Keywords

Multidimensional Scaling Monte Carlo Study Symmetric Component Asymmetric Component Proximity Relationship 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 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.CrossRefMATHGoogle Scholar
  2. 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
  3. 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.CrossRefMATHGoogle Scholar
  4. 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
  5. Okada, A. and Imaizumi, T. (1997). Asymmetric multidimensional scaling of two-mode three-way proximities. Journal of Classification, 14, 195–224.CrossRefMATHGoogle Scholar
  6. 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
  7. 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
  8. 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.CrossRefGoogle Scholar
  9. Zielman, B. (1991). Three-way scaling of asymmetric proximities. Research Report RR91–01, Department of Data Theory, University of Leiden, Leiden.Google Scholar
  10. Zielman, B. and Heiser, W. J. (1993). Analysis of asymmetry by a slide-vector. Psychometrika, 58, 101–114.CrossRefMATHGoogle Scholar

Copyright information

© Springer Japan 2002

Authors and Affiliations

  • Akinori Okada
    • 1
  • Tadashi Imaizumi
    • 2
  1. 1.Department of Industrial Relations, School of Social RelationsRikkyo (St. Paul’s) UniversityToshima-ku, TokyoJapan
  2. 2.Department of Management and Information SciencesTama UniversityTama City, TokyoJapan

Personalised recommendations