Skip to main content
SpringerLink
Log in

Multidimensional Scaling of Asymmetric Proximities with a Dominance Point

  • Conference paper
Advances in Data Analysis

Abstract

The purpose of the present study is to introduce a model and the associated nonmetric algorithm of multidimensional scaling for analyzing one-mode two-way (object × object) asymmetric proximities. In the model each object is represented as a point in a multidimensional Euclidean space, and a point, called the dominance point, is also embedded in the same multidimensional Euclidean space. The dominance point governs the asymmetry in the proximity relationships among objects, and represents the whole one-mode two-way asymmetric proximities dealt with in the analysis. An application to car switching data is presented.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 129.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 169.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  • BORG, I. and GROENEN, P.J.F. (2005): Modern Multidimensional Scaling. Springer, New York.

    MATH  Google Scholar 

  • CARROLL, J.D. and ARABIE, P. (1980): Multidimensional Scaling. In: M.R. Rosenzweig and L.W. Porter (Eds.): Annual Review of Psychology, 31. Annual Reviews, Palo Alto, 607–649.

    Google Scholar 

  • 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 

  • COOMBS, C.H. (1964): A Theory of Data. John Wiley, New York.

    Google Scholar 

  • CHINO, N., GROROUD, A. and YOSHINO, R. (1996): Complex Analysis of Two-Mode Three-Way Asymmetric Relational Data. Proceedings of the Fifth Conference of the International Federation of Classification Societies. 83–86.

    Google Scholar 

  • 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, 43–69.

    Article  MATH  Google Scholar 

  • HARSHMAN, R.A., GREEN, P.E., WIND, Y. and LUNDY, M.E. (1982): A Model for the Analysis of Asymmetric Data in Marketing Research. Marketing Science, 1, 205–242.

    Article  Google Scholar 

  • KRUSKAL, J.B. (1964): Nonmetric Multidimensional Scaling: A Numerical Method. Psychometrika, 29, 115–129.

    Article  MathSciNet  MATH  Google Scholar 

  • OKADA, A. (1988): Asymmetric Multidimensional Scaling of Car Switching Data. In: W. Gaul and M. Schader (Eds.): Data, Expert Knowledge and Decisions. Springer, Heidelberg, 279–290.

    Chapter  Google Scholar 

  • OKADA, A. and IMAIZUMI, T. (1987): Nonmetric Multidimensional Scaling of Asymmetric Proximities. Behaviormetrika, 21, 81–96.

    Article  Google Scholar 

  • OKADA, A. and IMAIZUMI, T. (1997): Asymmetric Multidimensional Scaling of Two-mode Three-way Proximities. Journal of Classification, 14, 95–224.

    Article  Google Scholar 

  • OKADA, A. and IMAIZUMI, T. (2003a): Joint Space Model for Multidimensional Scaling of Asymmetric Proximities. Abstracts of the 27th Annual Conference of the German Classification Society. 134.

    Google Scholar 

  • OKADA, A. and IMAIZUMI, T. (2003b): Asymmetric Multidimensional Scaling Based on Joint Space Model. Proceedings of the 13th International Meeting and the 68th Annual American Meeting of the Psychometric Society.

    Google Scholar 

  • OKADA, A. and IMAIZUMI, T. (2004): A Joint Space Model of Asymmetric Multidimensional Scaling. Proceedings of the International Meeting and the 69th Annual American Meeting of the Psychometric Society.

    Google Scholar 

  • OKADA, A. and IMAIZUMI, T. (2005): Joint Space Model for Multidimensional Scaling of Two-Mode Three-Way Asymmetric Proximities. In: D. Baier and K.-D. Wernecke (Eds.): Innovation in Classification, Data Science, and Information Systems. Springer, Berlin Heidelberg, 371–378.

    Chapter  Google Scholar 

  • ZIELMAN, B. (1991): Three-Way Scaling of Asymmetric Proximities. Research Report RR91-01. Department of Data Theory, University of 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 

  • ZIELMAN, B. and HEISER, W.J. (1996): Models for Asymmetric Proximities. British Journal of Mathematical and Statistical Psychology, 49, 127–146.

    Article  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Industrial Relations, School of Social Relations, Rikkyo (St. Paul’s) University, 3-34-1 Nishi Ikebukuro, Toshima-ku, Tokyo, 171-8501, Japan

    Akinori Okada

  2. School of Management and Information Sciences, Tama University, 4-4-1 Hijirigaoka, Tama city, Tokyo, 206-0022, Japan

    Tadashi Imaizumi

Authors
  1. Akinori Okada
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Tadashi Imaizumi
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Department of Business Administration and Economics, Bielefeld University, Universitätsstr. 25, 33501, Bielefeld, Germany

    Reinhold Decker

  2. Department of Economics, Freie Universität Berlin, Garystraße 21, 14195, Berlin, Germany

    Hans -J. Lenz

Rights and permissions

Reprints and permissions

Copyright information

© 2007 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Okada, A., Imaizumi, T. (2007). Multidimensional Scaling of Asymmetric Proximities with a Dominance Point. In: Decker, R., Lenz, H.J. (eds) Advances in Data Analysis. Studies in Classification, Data Analysis, and Knowledge Organization. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-70981-7_35

Download citation

Publish with us

Policies and ethics

Search

Navigation