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On the determination of appropriate dimensionality in data with error

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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 calledConstraint, is suggested.

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References

  • Beals, R., Krantz, D. H., & Tversky, A. Foundations of multidimensional scaling.Psychological Review, 1968,75, 127–142.

    Google Scholar 

  • Coombs, C. H., & Kao, R. C. On a connection between factor analysis and multidimensional unfolding.Psychometrika, 1960,25, 219–231.

    Google Scholar 

  • Klahr, D. A Monte Carlo investigation of the statistical significance of Kruskal's nonmetric scaling procedure.Psychometrika, 1969,34, 319–330.

    Google Scholar 

  • Kruskal, J. B. Multidimensional scaling by optimizing goodness of fit to a nonmetric hypothesis.Psychometrika, 1964,29, 1–27. (a)

    Google Scholar 

  • Kruskal, J. B. Nonmetric multidimensional scaling: A numerical method.Psychometrika, 1964,29, 115–129. (b)

    Google Scholar 

  • Ramsay, J. O. Some statistical considerations in multidimensional scaling.Psychometrika, 1969,34, 167–182.

    Google Scholar 

  • Shepard, R. N. Metric structures in ordinal data.Journal of Mathematical Psychology, 1966,3, 287–315.

    Google Scholar 

  • Spence, I. Multidimensional scaling: An empirical and theoretical investigation. Ph.D. dissertation, University of Toronto, 1970.

  • Stenson, H. H., & Knoll, R. L. Goodness of fit for random rankings in Kruskal's nonmetric scaling procedure.Psychological Bulletin, 1969,71, 122–126.

    Google Scholar 

  • Wagenaar, 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.

    Google Scholar 

  • Young, F. W. Nonmetric multidimensional scaling: Recovery of metric information.Psychometrika, 1970,35, 455–473.

    Google Scholar 

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Authors and Affiliations

  1. The Ohio State University, USA

    Paul D. Isaac & David D. S. Poor

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  1. Paul D. Isaac
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  2. David D. S. Poor
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Additional information

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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Isaac, P.D., Poor, D.D.S. On the determination of appropriate dimensionality in data with error. Psychometrika 39, 91–109 (1974). https://doi.org/10.1007/BF02291579

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  • DOI: https://doi.org/10.1007/BF02291579

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