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Joint Space Model for Multidimensional Scaling of Two-Mode Three-Way Asymmetric Proximities

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

Abstract

A joint space model and an associated nonmetric algorithm to analyze two-mode three-way asymmetric proximities (object × object × source) are presented. Each object is represented as a point and a circle (sphere, hyper sphere) in the common joint configuration which is common to all sources. Each source is represented as a point in the common joint configuration. For each source, the radius of an object is stretched or shrunk according to the distance between the dominance point representing the source and the point representing the object. An application to intergenerational occupational mobility data is shown.

Keywords

Multidimensional Scaling Occupational Category Nonmetric Multidimensional Scaling Orthogonal Rotation Joint Configuration 
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.

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References

  1. DESARBO, W.S., JOHNSON, M.D., MANRAI, A.K., MANRAI, L.A., and ED-WARD, E.A. (1992): TSCALE: A New Multidimensional Scaling Procedure Based on Tversky’s Contrast Model. Psychometrika, 57, 43–69.CrossRefGoogle Scholar
  2. KRUMHANSL, C.L. (1978): Concerning the Applicability of Geometric Model to Similarity Data: The Interrelationship between Similarity and Spatial Density. Psychological Review, 85, 445–463.CrossRefGoogle Scholar
  3. KRUSKAL, J.B. (1964): Nonmetric Multidimensional Scaling: A Numerical Method. Psychometrika, 29, 115–129.MATHMathSciNetCrossRefGoogle Scholar
  4. OKADA, A. and IMAIZUMI, T. (1987): Nonmetric Multidimensional Scaling of Asymmetric Proximities. Behaviormetrika, No. 21, 81–96.Google Scholar
  5. OKADA, A. and IMAIZUMI, T. (1997): Asymmetric Multidimensional Scaling of Two-Mode Three-Way Proximities. Journal of Classification, 14, 195–224.CrossRefGoogle Scholar
  6. OKADA, A. and IMAIZUMI, T. (2002): A Generalization of Two-Mode Three-Way Asymmetric Multidimensional Scaling. In: W. Gaul and G. Ritter (Eds.): Classification, Automation, and New Media. Springer, Berlin, 113–122.Google Scholar
  7. OKADA, A. and IMAIZUMI, T. (2003): Two-Mode Three-Way Nonmetric Multidimensional Scaling with Different Directions of Asymmetry for Different Sources. In: H. Yanai, A. Okada, K. Shigemasu, Y. Kano, and J.J. Meulman (Eds.): New Developments in Psychometrics. Springer, Tokyo, 495–502.Google Scholar
  8. SEIYAMA, K., NAOI, A., SATO, Y, TSUZUKI, K., and KOJIMA, H. (1990): Stratification Structure of Contemporary Japan and its Trend, In A. Naoi and K. Seiyama (Eds.): Social Stratification in Contemporary Japan Vol. 1. Structure and Process of Social Stratification. Tokyo University Press, Tokyo, 15–50. (in Japanese)Google Scholar
  9. ZIELMAN, B. (1991): Three-Way Scaling of Asymmetric Proximities. Research Report RR91-01, Department of Data Theory, University of Leiden.Google Scholar
  10. ZIELMAN, B. and HEISER, W.J. (1993): Analysis of Asymmetry by a Slide-Vector. Psychometrika, 58, 101–II4.CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin · Heidelberg 2005

Authors and Affiliations

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

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