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On the Determination of Appropriate Dimensionality in Data with Error

Published online by Cambridge University Press:  01 January 2025

Paul D. Isaac  and
David D. S. Poor
Paul D. Isaac
Affiliation:
The Ohio State University
David D. S. Poor
Affiliation:
The Ohio State University
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Abstract

The study deals with the problem of determining true dimensionality of data-with-error scaled by Kruskal's multidimensional scaling technique. Artificial data was constructed for 6, 8, 12, 16, and 30 point configurations of 1, 2, or 3 true dimensions by adding varying amounts of error to the true distances. Results show how stress is affected by error, number of points, and number of dimensions, and indicate that stress and the “elbow” criterion are inadequate for purposes of identifying true dimensionality when there is error in the data. The Wagenaar-Padmos procedure for identifying true dimensionality and error level is discussed. A simplified technique, involving a measure called Constraint, is suggested.

Keywords

Public PolicyStatistical TheoryMultidimensional ScalingError LevelScaling Technique
Type
Original Paper
Information
Psychometrika , Volume 39 , Issue 1 , March 1974 , pp. 91 - 109
Copyright
Copyright © 1974 The Psychometric Society

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Footnotes

*

The authors wish to thank Dr. J. B. Kruskal for his valuable help and suggestions.

†

Computer time for this research was supplied by the Instruction and Research Computer Center, The Ohio State University.

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