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.
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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. Murray Hill, N.J.: Bell Laboratories, 1973.
Young, F. W.A FORTRAN IV program for nonmetric multidimensional scaling (Report No. 56). Chapel Hill, N.C.: L. L. Thurstone Psychometric Laboratory, 1968.
Tschudi, F.The latent, the manifest and the reconstructed in multivariate data reduction models. Ph.D. Thesis, University of Oslo, 1972.
References
Arabie, P. Concerning Monte Carlo evaluations of nonmetric multidimensional scaling algorithms.Psychometrika, 1973,38, 607–608.
Arabie, P. Random versus rational strategies for initial configurations in nonmetric multidimensional scaling.Psychometrika 1978,43, 000–000.
Clark, A. K. Re-evaluation of Monte Carlo studies in nonmetric multi-dimensional scaling.Psychometrika, 1976,41, 401–404.
Klahr, D. A Monte Carlo investigation of the statistical significance of Kruskal's scaling procedure.Psychometrika, 1969,34, 319–330.
Lingoes, J. C., & Roskam, E. E. A mathematical and empirical analysis of two multidimensional scaling algorithms.Psychometric Monograph Supplement, 1973,38 (1, Pt. 2).
Shepard, R. N. Representation of structure in similarity data: Problems and prospects.Psychometrika, 1974,39, 373–421.
Spence, I. A Monte Carlo evaluation of three nonmetric multidimensional scaling algorithms.Psychometrika, 1972,37, 461–486.
Spence, I. On random rankings studies in nonmetric scaling.Psychometrika, 1974,39, 267–268.
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.
Stenson, H. H., & Knoll, R. L. Goodness of fit for random rankings in Kruskal's nonmetric scaling procedure.Psychological Bulletin, 1969,72, 122–126.
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.
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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.
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Spence, I., Young, F.W. Monte Carlo studies in nonmetric scaling. Psychometrika 43, 115–117 (1978). https://doi.org/10.1007/BF02294095
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DOI: https://doi.org/10.1007/BF02294095