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Nonmetric Multidimensional Scaling of Asymmetric Proximities

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Abstract

Nonmetric multidimensional scaling which could be applied to a square asymmetric inter-stimulus proximity matrix is presented. In the model each stimulus is represented as a point and a circle (sphere, hypersphere) whose center is at that point in a multidimensional Euclidean space. The radius of a circle (sphere, hypersphere) tells the skew-symmetry of the corresponding stimulus. In a sense the model is a nonmetric generalization of Weeks and Bentler (1982) ’s model. An algorithm to derive the coordinates of points and radii of circles (spheres, hypers-pheres) which minimize the discrepancy of the coordinates and radii from the monotone relationship with given interstimulus proximities is described. An application to car switching data among 16 car segments is represented.

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Authors and Affiliations

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

    Akinori Okada & Tadashi Imaizumi

Authors
  1. Akinori Okada
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  2. Tadashi Imaizumi
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Additional information

This work was supported by a grant from the Rikkyo (St. Paul’s) University Research Fund. The authors would like to express their gratitude to The Institute of Management Sciences and the authors of “A model for the analysis of asymmetric data in marketing research” by R.A. Harshman, P.E. Green, Y. Wind, and M. Lundy, 1982, Marketing Science, 1, 205–242 for permitting and approving to adopt their tables. Request of reprints should be made to the first author.

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Okada, A., Imaizumi, T. Nonmetric Multidimensional Scaling of Asymmetric Proximities. Behaviormetrika 14, 81–96 (1987). https://doi.org/10.2333/bhmk.14.21_81

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  • DOI: https://doi.org/10.2333/bhmk.14.21_81

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