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Robust Multidimensional Scaling

Published online by Cambridge University Press:  01 January 2025

Ian Spence  and
Stephan Lewandowsky
Ian Spence*
Affiliation:
University of Toronto
Stephan Lewandowsky
Affiliation:
University of Toronto
*
Requests for reprints should be sent to the first author at the Department of Psychology, University of Toronto, Toronto, Ontario, CANADA M5S 1A1.
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Abstract

A method for multidimensional scaling that is highly resistant to the effects of outliers is described. To illustrate the efficacy of the procedure, some Monte Carlo simulation results are presented. The method is shown to perform well when outliers are present, even in relatively large numbers, and also to perform comparably to other approaches when no outliers are present.

Keywords

multidimensional scalingrobust estimationoutliers
Type
Original Paper
Information
Psychometrika , Volume 54 , Issue 3 , September 1989 , pp. 501 - 513
Copyright
Copyright © 1989 The Psychometric Society

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Footnotes

This research was supported by Grant A8351 from the Natural Sciences and Engineering Research Council of Canada to Ian Spence.

References

Edwards, D. R. (1986, June). Graphical artifacts in multidimensional scaling. Paper presented at a meeting of the Psychometric Society, Toronto.Google Scholar
Heiser, W. J. (1987, July). Multidimensional scaling with least absolute residuals. Presented at the First Conference of the International Federation of Classification Societies, Aachen, Federal Republic of Germany.Google Scholar
Huber, P. J. (1981). Robust statistics, New York: Wiley.CrossRefGoogle Scholar
IMSL (1980). IMSL library reference manual 8th ed.,, Houston, TX: Author.Google Scholar
Knuth, D. E. (1969). The art of computer programming: Seminumerical algorithms (Vol. 2), Reading, MA: Addison-Wesley.Google Scholar
Kruskal, J. B., Young, F. W., & Seery, J. B. (1978). How to use KYST-2, a very flexible program to do multidimensional scaling and unfolding, Murray Hill, NJ: Bell Laboratories.Google Scholar
Luenberger, D. G. (1984). Linear and nonlinear programming 2nd ed.,, Reading, MA: Addison-Wesley.Google Scholar
Mosteller, F. & Tukey, J. W. (1977). Data analysis and regression, Reading, MA: Addison-Wesley.Google Scholar
Null, C. H., & Sarle, W. (1982, June). Robust multidimensional scaling. Paper presented at the Joint Meeting of the Psychometric and Classification Societies, Montreal, Canada.Google Scholar
Ramsay, J. O. (1975). Solving implicit equations in psychometric data analysis. Psychometrika, 40, 337–360.CrossRefGoogle Scholar
Ramsay, J. O. (1977). Maximum likelihood estimation in multidimensional scaling. Psychometrika, 42, 241–266.CrossRefGoogle Scholar
Ramsay, J. O. (1982). Multiscale II manual, Montreal: McGill University.Google Scholar
Spence, I. (1972). A Monte Carlo evaluation of three nonmetric multidimensional scaling algorithms. Psychometrika, 37, 461–486.CrossRefGoogle Scholar
Spence, I. (1982, June). Robust multidimensional scaling. Paper presented at the Joint Meeting of the Psychometric and Classification Societies, Montreal, Canada.Google Scholar
Spence, I. (1983). Monte Carlo simulation studies. Applied Psychological Measurement, 7, 405–425.CrossRefGoogle Scholar
Takane, Y., Young, F. W., & de Leeuw, J. (1977). Nonmetric individual differences multidimensional scaling: An alternating least squares method with optimal scaling features. Psychometrika, 42, 7–67.CrossRefGoogle Scholar
Torgerson, W. S. (1958). Theory and methods of scaling, New York: Wiley.Google Scholar
Young, F. W. (1970). Nonmetric multidimensional scaling: Recovery of metric information. Psychometrika, 35, 455–473.CrossRefGoogle Scholar
Young, F. W., & Lewyckyj, R. (1981). ALSCAL 4 user's guide, Chapel Hill, NC: Data Analysis and Theory Associates.Google Scholar
Young, G., & Householder, A. S. (1938). Discussion of a set of points in terms of their mutual distances. Psychometrika, 3, 19–21.CrossRefGoogle Scholar
Zinnes, J. L., & MacKay, D. B. (1983). Probabilistic multidimensional scaling: Complete and incomplete data. Psychometrika, 48, 27–48.CrossRefGoogle Scholar