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The Additive Constant Problem in Multidimensional Scaling

Published online by Cambridge University Press:  01 January 2025

Samuel J. Messick  and
Robert P. Abelson
Samuel J. Messick
Affiliation:
Educational Testing Service
Robert P. Abelson
Affiliation:
Yale University
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Abstract

The problem of choosing the correct additive constant to convert relative interstimulus distances to absolute interstimulus distances in multidimensional scaling is investigated. An artificial numerical example is constructed, and various trial values of the constant are inserted to demonstrate the effect on the multidimensional map of making a variety of incorrect choices. Finally, a general solution to the problem, suggested by Dr. Ledyard R Tucker, is presented; each of the computational steps in this solution is set down for easy reference.

Information

Type
Original Paper
Information
Psychometrika , Volume 21 , Issue 1 , March 1956 , pp. 1 - 15
Copyright
Copyright © 1956 The Psychometric Society

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Footnotes

*

This study was supported in part by Office of Naval Research Contract N6onr-270-20 and by National Science Foundation Grant G-642 to Princeton University.

†

Now at Menninger Foundation.

References

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