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Monte Carlo Studies in Nonmetric Scaling

Published online by Cambridge University Press:  01 January 2025

Ian Spence  and
Forrest W. Young
Ian Spence*
Affiliation:
University of Western Ontario
Forrest W. Young
Affiliation:
University of North Carolina
*
Requests for reprints should be sent to I. Spence, Department of Psychology, University of Western Ontario, London, Ontario N6A 5C2, CANADA.
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Abstract

In response to Arabie several random ranking studies are compared and discussed. Differences are typically very small, however it is noted that those studies which used arbitrary configurations tend to produce slightly higher stress values. The choice of starting configuration is discussed and we suggest that the use of a principal components decomposition of the doubly centered matrix of dissimilarities, or some transformation thereof, will yield an initial configuration which is superior to a randomly chosen one.

Keywords

multidimensional scalingrandom rankingsinitial configuration
Type
Notes and Comments
Information
Psychometrika , Volume 43 , Issue 1 , March 1978 , pp. 115 - 117
Copyright
Copyright © 1978 The Psychometric Society

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Footnotes

This research was supported by the National Research Council of Canada (Grant No. A8351) and by the National Institute of Mental Health (Grant Nos. MH10006 and MH26504). The authorship order has been determined by Monte Carlo methods.

References

Reference Notes

Kruskal, J. B., Young, F. W., & Seery, J. B. How to use KYST, a very flexible program to do multidimensional scaling and unfolding, 1973, Murray Hill, N.J.: Bell Laboratories.Google Scholar
Young, F. W. A FORTRAN IV program for nonmetric multidimensional scaling (Report No. 56), 1968, Chapel Hill, N.C.: L. L. Thurstone Psychometric Laboratory.Google Scholar
Tschudi, F. The latent, the manifest and the reconstructed in multivariate data reduction models. Ph.D. Thesis, University of Oslo, 1972.Google Scholar

References

Arabie, P. Concerning Monte Carlo evaluations of nonmetric multidimensional scaling algorithms. Psychometrika, 1973, 38, 607–608.CrossRefGoogle Scholar
Arabie, P. Random versus rational strategies for initial configurations in nonmetric multidimensional scaling. Psychometrika, 1978, 43, 000–000.CrossRefGoogle Scholar
Clark, A. K. Re-evaluation of Monte Carlo studies in nonmetric multi-dimensional scaling. Psychometrika, 1976, 41, 401–404.CrossRefGoogle Scholar
Klahr, D. A Monte Carlo investigation of the statistical significance of Kruskal's scaling procedure. Psychometrika, 1969, 34, 319–330.CrossRefGoogle Scholar
Lingoes, J. C., & Roskam, E. E. A mathematical and empirical analysis of two multidimensional scaling algorithms. Psychometric Monograph Supplement, 1973, 38 (1, Pt. 2).Google Scholar
Shepard, R. N. Representation of structure in similarity data: Problems and prospects. Psychometrika, 1974, 39, 373–421.CrossRefGoogle Scholar
Spence, I. A Monte Carlo evaluation of three nonmetric multidimensional scaling algorithms. Psychometrika, 1972, 37, 461–486.CrossRefGoogle Scholar
Spence, I. On random rankings studies in nonmetric scaling. Psychometrika, 1974, 39, 267–268.CrossRefGoogle Scholar
Spence, I., & Ogilvie, J. C. A table of expected stress values for random rankings in nonmetric multidimensional scaling. Multivariate Behavioral Research, 1973, 8, 511–517.CrossRefGoogle ScholarPubMed
Stenson, H. H., & Knoll, R. L. Goodness of fit for random rankings in Kruskal's nonmetric scaling procedure. Psychological Bulletin, 1969, 72, 122–126.CrossRefGoogle Scholar
Wagemaar, W. A., & Padmos, P. Quantitative interpretation of stress in Kruskal's multidimensional scaling technique. British Journal of Mathematical and Statistical Psychology, 1971, 24, 101–110.CrossRefGoogle Scholar