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Nonmetric Multidimensional Scaling: Recovery of Metric Information

Published online by Cambridge University Press:  01 January 2025

Forrest W. Young
Forrest W. Young*
Affiliation:
University of North Carolina
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Abstract

The degree of metric determinancy afforded by nonmetric multidimensional scaling was investigated as a function of the number of points being scaled, the true dimensionality of the data being scaled, and the amount of error contained in the data being scaled. It was found 1) that if the ratio of the degrees of freedom of the data to that of the coordinates is sufficiently large then metric information is recovered even when random error is present; and 2) when the number of points being scaled increases the stress of the solution increases even though the degree of metric determinacy increases.

Type
Original Paper
Information
Psychometrika , Volume 35 , Issue 4 , December 1970 , pp. 455 - 473
Copyright
Copyright © 1970 The Psychometric Society

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Footnotes

*

This report was supported in part by a PHS research grant No. M-10006 from the National Institute of Mental Health, Public Health Service, and in part by a Science Development grant No. GU-2059, from the National Science Foundation. The author is indebted to Charles R. Sherman for his assistance in gathering the data and for his critical re-writing of sections of this report. The assistance of Lyle V. Jones in his critical readings and comments is also deeply appreciated.

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