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Nonmetric Multidimensional Scaling: A Monte Carlo Study of the Basic Parameters

Published online by Cambridge University Press:  01 January 2025

Charles R. Sherman
Charles R. Sherman*
Affiliation:
University of North Carolina
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Abstract

Metric determinacy of nonmetric multidimensional scaling was investigated as a function of the number of points being scaled, the amount of error in the data being scaled, and the accuracy of estimation of the Minkowski distance function parameters, dimensionality and the r-constant. It was found that nonmetric scaling may provide better models if (1) the true structure is of low dimensionality, (2) the dimensionality of recovered structure is not less than the dimensionality of the true structure, (3) degree of error is low, and (4) the degrees of freedom ratio is greater than about 2.5. It was also found that (5) accurate estimation of the Minkowski constant leads to a better model only if the dimensionality has been properly estimated.

Keywords

Public PolicyDistance FunctionAccurate EstimationStatistical TheoryFunction Parameter
Type
Original Paper
Information
Psychometrika , Volume 37 , Issue 3 , September 1972 , pp. 323 - 355
Copyright
Copyright © 1972 The Psychometric Society

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Footnotes

*

This report is based on a thesis submitted in partial fulfillment of the degree of Master of Arts at the University of North Carolina, April, 1970. The thesis is an outgrowth of earlier work done with Forrest W. Young. The author is indebted to Forrest W. Young, Norman Cliff, and Lyle V. Jones for their assistance in the preparation of this report. This report was supported in part by PHS research grant No. M-10006 from the National Institute of Mental Health, Public Health Service.

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