Abstract
The degree of metric determinancy afforded by nonmetric multidimensional scaling was investigated as a function of the number of points being scaled, the true dimensionality of the data being scaled, and the amount of error contained in the data being scaled. It was found 1) that if the ratio of the degrees of freedom of the data to that of the coordinates is sufficiently large then metric information is recovered even when random error is present; and 2) when the number of points being scaled increases the stress of the solution increases even though the degree of metric determinacy increases.
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References
Bock, R. D. & Jones, L. V.The measurement and prediction of judgment and choice. San Francisco: Holden Day, 1968.
Coombs, C. H. & Kao, R. C. On a connection between factor analysis and multidimensional unfolding.Psychometrika, 1960,25, 219–231.
Guttman, L. The development of nonmetric space analysis: A letter to Professor John Ross.Multivariate Behavioral Research, 1967,2, 71–82.
Kruskal, J. B. Multidimensional scaling by optimizing goodness-of-fit to a nonmetric hypothesis.Psychometrika, 1964a,29, 1–28.
Kruskal, J. B. Nonmetric multidimensional scaling: a numerical method.Psychometrika, 1964b,29, 115–130.
Lingoes, J. C. An IBM-7090 program for Guttman-Lingoes smallest space analysis—RI.Behavioral Science, 1966,11, 332.
McGee, V. E. The multidimensional analysis of ‘elastic’ distances.The British Journal of Mathematical and Statistical Psychology, 1966,19, 181–196.
Ramsay, J. Some statistical considerations in multidimensional scaling. Psychometrika, 1969,34, 167–182.
Shepard, R. N. The analysis of proximities: multidimensional scaling with an unknown distance function: I.Psychometrika, 1962a,27, 125–140.
Shepard, R. N. The analysis of proximities: multidimensional scaling with an unknown distance function: II.Psychometrika, 1962b,27, 219–246
Shepard, R. N. Metric structures in ordinal data.Journal of Mathematical Psychology, 1966,3, 287–315.
Sherman, C. R. and Young, F. W. Nonmetric multidimensional scaling: A monte carlo study.Proceedings of the 76th Annual Convention of the American Psychological Association, 1968,3, 207–208.
Thurstone, L. L. A law of comparative judgment.Psychological Review, 1927,34, 273–286.
Torgerson, W. S.Theory and methods of scaling. New York: Wiley, 1958.
Young, F. W. TORSCA-9, A FORTRAN IV program for nonmetric multi-dimensional scaling.Behavioral Science, 1968,13, 343–344.
Young, F. W. & Torgerson, W. S. TORSCA, A FORTRAN IV program for Shepard-Kruskal multidimensional scaling analysis.Behavioral Science, 1967,12, 498.
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This report was supported in part by a PHS research grant No. M-10006 from the National Institute of Mental Health, Public Health Service, and in part by a Science Development grant No. GU-2059, from the National Science Foundation. The author is indebted to Charles R. Sherman for his assistance in gathering the data and for his critical re-writing of sections of this report. The assistance of Lyle V. Jones in his critical readings and comments is also deeply appreciated.
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Young, F.W. Nonmetric multidimensional scaling: Recovery of metric information. Psychometrika 35, 455–473 (1970). https://doi.org/10.1007/BF02291820
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DOI: https://doi.org/10.1007/BF02291820