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The Effects of Random Error and Subsampling of Dimensions on Recovery of Configurations by Non-Metric Multidimensional Scaling

Published online by Cambridge University Press:  01 January 2025

Harvey S. Cohen  and
Lawrence E. Jones
Harvey S. Cohen
Affiliation:
University of Illinois at Urbana-Champaign
Lawrence E. Jones
Affiliation:
University of Illinois at Urbana-Champaign
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Abstract

Similarity judgments of three-dimensional stimuli were simulated, with the hypothetical subject attending to only some dimensions of stimulus variation (i.e., “subsampling”) on each trial. Recovery of the stimulus configuration by non-metric multidimensional scaling was investigated as a function of subsampling, the amount of random error in the judgments, and the number of stimuli being scaled.

It was found that: (1) dimensions to which the subject often attends were well recovered even when dimensions seldom attended to were not, and (2) measures of recovery based on interpoint distances were inadequate. Several previous Monte Carlo studies were evaluated in light of the results.

Keywords

Public PolicyRandom ErrorStatistical TheoryMultidimensional ScalingMonte Carlo Study
Type
Original Paper
Information
Psychometrika , Volume 39 , Issue 1 , March 1974 , pp. 69 - 90
Copyright
Copyright © 1974 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 Illinois. The thesis is an outgrowth of earlier work presented in Cohen, H. S., Wing, P. L., & Jones, L. E. The effects of error and subsampling of dimensions on multidimensional scaling solutions. Mathematical Psychology Meetings, Princeton, September, 1971.

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