Two-Mode Three-Way Asymmetric Multidimensional Scaling with Constraints on Asymmetry

  • A. Okada
  • T. Imaizumi
Part of the Studies in Classification, Data Analysis, and Knowledge Organization book series (STUDIES CLASS)

Abstract

A model and an accompanying algorithm for two-mode three-way asymmetric multidimensional scaling is presented. The present model has a constraint on asymmetry, compared with the model of Okada, Imaizumi (1997) where each source has a different magnitude of asymmetry, but all sources are constrained so that the relative importance of the asymmetry along dimensions is constant for all sources. The accompanying nonmetric algorithm was developed from similar work in Okada, Imaizumi (1997). An application to interpersonal attraction data among university students is presented.

Keywords

Tama 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Arabie, P. (1978): Random versus Rational Strategies for Initial Configurations in Nonmetric Multidimensional Scaling. Psychometrika, 43, 111–113.CrossRefGoogle Scholar
  2. Arabie, P., Carroll, J.D., and DeSarbo, W.S. (1987): Three-way Scaling and Clustering. Sage, Newbury Park, CA. Translated into Japanese by A. Okada and T. Imaizumi (1990), Tokyo: Kyoritsu Shuppan. Software named Three-way Scaling is associated with the translation.Google Scholar
  3. Breiger, R.L., Boorman, S.A., and Arabie, P. (1975): An Algorithm for Clustering Relational Data with Applications to Social Network Analysis and Comparison with Multidimensional Scaling. Journal of Mathematical Psychology, 12, 328–383.CrossRefGoogle Scholar
  4. Carroll, J.D. (1985): [Review of Multidimensional Scaling]. Psychometrika, 50, 133–140.CrossRefGoogle Scholar
  5. 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.CrossRefGoogle Scholar
  6. Chino, N., Groruid, A., and Yoshino, R. (1996): A Complex Analysis for Two-Mode Three-Way Asymmetric Relational Data. Proceedings of the Fifth Conference of the International Federation of Classification Societies at Kobe, Japan (vol. 2), 83–86.Google Scholar
  7. DeSarbo W.S. Johnson M.D. Manrai A.K. Manrai L.A. and Edward E.A. 1992 TSCALE A New Multidimensional Scaling Procedure Based on Tversky’s Contrast Model. Psychometrika 57 43–69CrossRefGoogle Scholar
  8. Kruskal, J.B. and Carroll, J.D. (1969): Geometric Models and Badness-of-fit Measures. In: P.K. Krishnaiah (ed.): Multivariate Analysis. Academic Press, New York, 639–671.Google Scholar
  9. Nakao, K. and Romney, A.K. (1993): Longitudinal Approach to Subgroup Formation: Reanalysis of Newcomb’s Fraternity Data. Social Networks, 15, 109–131.CrossRefGoogle Scholar
  10. Newcomb, T. M. (1979): Reciprocity of Interpersonal Attraction: A Nonconfirmation of a Plausible Hypothesis. Social Psychology Quarterly, 42, 299–306.CrossRefGoogle Scholar
  11. Nordlie, P. G. (1958): A Longitudinal Study of Interpersonal Attraction in a Natural Group Setting. Doctoral dissertation, University of Michigan.Google Scholar
  12. Okada, A. and Imaizumi, T. (1997): Asymmetric Multidimensional Scaling of Two-Mode Three-Way Proximities. Journal of Classification, 14, 195–224.CrossRefGoogle Scholar
  13. Zielman, B. (1991): Three-Way Scaling of Asymmetric Proximities. Research Report RR91-01, Department of Data Theory, University of Leiden.Google Scholar
  14. Zielman, B. and Heiser, W. J. (1993): Analysis of Asymmetry by a Slide-Vector. Psychometrika, 58, 101–114.CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2000

Authors and Affiliations

  • A. Okada
    • 1
  • T. Imaizumi
    • 2
  1. 1.Department of Industrial RelationsSchool of Social Relations Rikkyo (St. Paul’s) UniversityToshima-kuJapan
  2. 2.Tama UniversityTama CityJapan

Personalised recommendations