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On metric multidimensional unfolding

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Abstract

The problem of locating two sets of points in a joint space, given the Euclidean distances between elements from distinct sets, is solved algebraically. For error free data the solution is exact, for fallible data it has least squares properties.

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References

  • Bennett, J. F. Determination of the number of independent parameters of a score matrix from the examination of rank orders.Psychometrika, 1956,21, 383–393.

    Article  Google Scholar 

  • Bennett, J. F., & Hays, W. L. Multidimensional unfolding: Determining the dimensionality of ranked preference data.Psychometrika, 1960,25, 27–43.

    Article  Google Scholar 

  • Bloxom, B. Individual differences in multidimensional scaling. ETS Research Bulletin 68-45. Princeton: Educational Testing Service, 1968.

    Google Scholar 

  • Carroll, J. D., & Chang, Jih-Jie. Relating preference data to multidimensional scaling solutions via a generalization of Coombs' unfolding model. Paper read at the Spring Meeting of the Psychometric Society, Madison, Wisconsin, 1967.

  • Carroll, J. D., & Chang, Jih-Jie. Analysis of individual differences in multidimensional scaling via an N-way generalization of “Eckart-Young” decomposition.Psychometrika, 1970,35, 283–319.

    Google Scholar 

  • Coombs, C. H. Inconsistencies of preferences in psychological measurement.Journal of Experimental Psychology, 1958,55, 1–7.

    PubMed  Google Scholar 

  • Coombs, C. H.A theory of data. New York: Wiley, 1964.

    Google Scholar 

  • Coombs, C. H., & Kao, R. C. Nonmetric factor analysis. Department of Engineering Research Bulletin No. 38. Ann Arbor: University of Michigan, 1955.

    Google Scholar 

  • Eckart, C., & Young, G. The approximation of one matrix by another of lower rank.Psychometrika, 1936,1, 211–218.

    Article  Google Scholar 

  • Goode, F. M. Interval scale representation of ordered metric scales. Dittoed manuscript, University of Michigan, 1957.

  • Hays, W. L., & Bennett, J. F. Multidimensional unfolding: Determining configuration from complete rank order preference data.Psychometrika, 1961,26, 221–238.

    Article  Google Scholar 

  • Krantz, D. H. Rational distances functions for multidimensional scaling.Journal of Mathematical Psychology, 1967,4, 226–244.

    Article  Google Scholar 

  • Kruskal, J. B. How to use MDSCAL, a program to do multidimensional scaling and multidimensional unfolding. Unpublished report, Bell Telephone Laboratories, 1968.

  • Lingoes, J. C. A general nonparametric model for representing objects and attributes in a joint space. In J. C. Gardin (Ed.),Les Comptes-rendus de Colloque International sur L'emploi des Calculateurs en Archeologie: Problèmes Sémiologiques et Mathématiques. Marseilles: Centre Nationale de la Recherche Scientifiques, in press.

  • Ross, J., & Cliff, N. A generalization of the interpoint distance model.Psychometrika, 1964,29, 167–176.

    Google Scholar 

  • Schonemann, P. H. Fitting a simplex symmetrically.Psychometrika, 1970,35, 1–21.

    Google Scholar 

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  1. Peter H. Schönemann

    Present address: Purdue University, USA

Authors and Affiliations

  1. The Ohio State University, USA

    Peter H. Schönemann

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  1. Peter H. Schönemann
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Schönemann, P.H. On metric multidimensional unfolding. Psychometrika 35, 349–366 (1970). https://doi.org/10.1007/BF02310794

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  • DOI: https://doi.org/10.1007/BF02310794

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