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Restricted Multidimensional Scaling Models for Asymmetric Proximities

Published online by Cambridge University Press:  01 January 2025

David G. Weeks  and
P. M. Bentler
David G. Weeks*
Affiliation:
Washington University School of Medicine
P. M. Bentler
Affiliation:
University of California, Los Angeles
*
Requests for reprints should be sent to David G. Weeks, Washington University School of Medicine, 369 North Taylor, St. Louis, Missouri 63108.
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Abstract

Restricted multidimensional scaling models [Bentler & Weeks, 1978] allowing constraints on parameters, are extended to the case of asymmetric data. Separate functions are used to model the symmetric and antisymmetric parts of the data. The approach is also extended to the case in which data are presumed to be linearly related to squared distances. Examples of several models are provided, using journal citation data. Possible extensions of the models are considered.

Keywords

multidimensional scalingasymmetric data
Type
Original Paper
Information
Psychometrika , Volume 47 , Issue 2 , June 1982 , pp. 201 - 208
Copyright
Copyright © 1982 The Psychometric Society

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Footnotes

This research was supported in part by USPHS Grant 0A01070, P. M. Bentler, principal investigator, and NIMH Grant MH-24819, E. J. Anthony and J. Worland, principal investigators.

The authors wish to thank E. W. Holman and several anonymous reviewers for their valuable suggestions concerning this research.

References

Reference Notes

Chino, N. A unified geometrical interpretation of the MDS techniques for the analysis of asymmetry and related techniques. Paper presented at the meeting of the Psychometric Society, Iowa City, May, 1980.Google Scholar
Harshman, R. S. Models for analysis of symmetrical relationships among N objects or stimuli. Paper presented at the meeting of the Psychometric Society and the Society for Mathematical Psychology, McMaster University, Hamilton, Ontario, August, 1978.Google Scholar
Hutchinson, J. W. Network representations of asymmetric data. Paper presented at the Berkeley-Stanford joint meeting in Biological and Cognitive Psychology, Stanford, May, 1980.Google Scholar
Young, F. W. An asymmetric euclidean model for multi-process asymmetric data. Proceedings of the U.S.-Japan Seminar, University of California, San Diego, August, 1975.Google Scholar

References

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