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A Note on the use of Directional Statistics in Weighted Euclidean Distances Multidimensional Scaling Models

Published online by Cambridge University Press:  01 January 2025

Charles L. Jones
Charles L. Jones*
Affiliation:
McMaster University and University of Toronto
*
Reprint requests should be addressed to Charles L. Jones, Sociology Department, 563 Spadina Avenue, University of Toronto, Toronto, Ontario, M5S 1A1, Canada.
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Abstract

The weighted euclidean distances model in multidimensional scaling (WMDS) represents individual differences as dimension saliences which can be interpreted as the orientations of vectors in a subject space. It has recently been suggested that the statistics of directions would be appropriate for carrying out tests of location with such data. The nature of the directional representation in WMDS is reviewed and it is argued that since dimension saliences are almost always positive, the directional representations will usually be confined to the positive orthant. Conventional statistical techniques are appropriate to angular representations of the individual differences which will yield angles in the interval (0, 90) so long as dimension saliences are nonnegative, a restriction which can be imposed. Ordinary statistical methods are also appropriate with several linear indices which can be derived from WMDS results. Directional statistics may be applied more fruitfully to vector representations of preferences.

Keywords

multidimensional scalingdirectional data
Type
Notes And Comments
Information
Psychometrika , Volume 48 , Issue 3 , September 1983 , pp. 473 - 476
Copyright
Copyright © 1983 The Psychometric Society

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Footnotes

Material support for work referred to herein was received from SSRC grant HR 1883/1, SSHRC grant 410-77-0860, and from McMaster University.

Thanks are due to A. P. M. Coxon, M. J. Prentice, M. A. Stephens and an anonymous reviewer.

References

Reference Notes

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