Hostname: page-component-745bb68f8f-v2bm5 Total loading time: 0 Render date: 2025-01-08T04:29:24.836Z Has data issue: false hasContentIssue false
  • English
  • Français

Scaling and Psychometrika: Spatial and Alternative Representations of Similarity Data

Published online by Cambridge University Press:  01 January 2025

Warren S. Torgerson
Warren S. Torgerson*
Affiliation:
The Johns Hopkins University
*
Requests for reprints should be sent to Warren S. Torgerson, Department of Psychology, The Johns Hopkins University, Baltimore, MD 21218.
Get access Rights & Permissions [Opens in a new window]

Abstract

Progress over the past twenty-five years in the development and improvement of models for representation of similarity data is reviewed. The discussion includes comments on class, dimensional, ideal type, and dichotomous attribute representations of underlying similarity structures. Most of the theoretical research in the area appeared, and continues to appear, in Psychometrika.

Type
50th Anniversary Section
Information
Psychometrika , Volume 51 , Issue 1 , March 1986 , pp. 57 - 63
Copyright
Copyright © 1986 The Psychometric Society

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Arabie, P., Carroll, J. D. (1980). MAPCLUS: A mathematical programming approach to fitting the ADCLUS model. Psychometrika, 45, 211–235.CrossRefGoogle Scholar
Attneave, F. (1950). Dimensions of similarity. American Journal of Psychology, 63, 516–556.CrossRefGoogle ScholarPubMed
Bennett, R. S. (1969). The intrinsic dimensionality of signal collections. IEEE Transactions on Information Theory, 517–525.CrossRefGoogle Scholar
Bloxom, B. (1974). An alternative method of fitting a model of individual differences in multidimensional scaling. Psychometrika, 39, 365–367.CrossRefGoogle Scholar
Carroll, J. D. (1976). Spatial, non-spatial and hybrid models for scaling. Psychometrika, 41, 439–463.CrossRefGoogle Scholar
Carroll, J. D., Chang, J. J. (1970). Analysis of individual differences in multidimensional scaling via anN-way generalization of “Eckart-Young” decomposition. Psychometrika, 35, 283–319.CrossRefGoogle Scholar
Carroll, J. D., & Chang, J. J. (1972, April). IDIOSCAL Individual Differences in Orientation Scaling. Paper presented at the spring meeting of the Psychometric Society, Princeton, NJ.Google Scholar
Carroll, J. D., Pruzansky, S. (1980). Discrete and hybrid scaling models. In Lanterman, E. D., Feger, H. (Eds.), Proceedings of Aachen Symposia on Decision Making and Multidimensional Scaling, Berlin: Springer-Verlag.Google Scholar
Degerman, R. (1970). Multidimensional analysis of complex structure: Mixtures of class and quantitative variation. Psychometrika, 35, 475–491.CrossRefGoogle Scholar
Ekman, G. (1954). Dimensions of color vision. Journal of Psychology, 38, 467–474.CrossRefGoogle Scholar
Girard, R. A., Cliff, N. (1976). A Monte Carlo evaluation of interactive multidimensional scaling. Psychometrika, 41, 43–64.CrossRefGoogle Scholar
Holman, E. W. (1972). The relations between hierarchical and Euclidean models for psychological distances. Psychometrika, 37, 417–423.CrossRefGoogle Scholar
Horan, C. B. (1969). Multidimensional scaling: Combining observations when individuals have different perceptual structures. Psychometrika, 34, 139–165.CrossRefGoogle Scholar
Johnson, S. C. (1967). Hierarchical clustering schemes. Psychometrika, 32, 241–254.CrossRefGoogle ScholarPubMed
Kaiser, H. F. (1958). The varimax criterion for analytic rotation in factor analysis. Psychometrika, 23, 187–200.CrossRefGoogle Scholar
Kruskal, J. B. (1964). Multidimensional scaling by optimizing goodness of fit to a nonmetric hypothesis. Psychometrika, 29, 1–27.CrossRefGoogle Scholar
Kruskal, J. B. (1964). Nonmetric multidimensional scaling: A numerical method. Psychometrika, 29, 115–129.CrossRefGoogle Scholar
Lingoes, J. C. (1965). An IBM program for Guttman-Lingoes smallest space analysis. Behavioral Science, 10, 183–184.Google Scholar
MacCallum, R. C. (1976). Effects on INDSCAL of non-orthogonal perceptions of object space dimensions. Psychometrika, 41, 177–188.CrossRefGoogle Scholar
MacCallum, R. C. (1977). Effects on conditionality of INDSCAL and ALSCAL weights. Psychometrika, 42, 297–305.CrossRefGoogle Scholar
MacCallum, R. C. (1979). Recovery of structure in incomplete data by ALSCAL. Psychometrika, 44, 69–74.CrossRefGoogle Scholar
MacCallum, R. C., Cornelius, E. T. III (1977). A Monte Carlo investigation of recovery of structure by ALSCAL. Psychometrika, 42, 401–428.CrossRefGoogle Scholar
McGee, V. E. (1968). Multidimensional scaling ofN sets of similarity measures: A nonmetric individual differences approach. Multivariate Behavioral Research, 3, 233–248.CrossRefGoogle Scholar
Sattath, S., Tversky, A. (1977). Additive similarity trees. Psychometrika, 42, 319–345.CrossRefGoogle Scholar
Sheldon, W. H., Stevens, S. S. (1942). The Varieties of Temperament, New York: Harper.Google Scholar
Shepard, R. N. (1962). The analysis of proximities: Multidimensional scaling with an unknown distance function. I. Psychometrika, 27, 125–140.CrossRefGoogle Scholar
Shepard, R. N. (1962). The analysis of proximities: Multidimensional scaling with an unknown distance function. II. Psychometrika, 27, 219–246.CrossRefGoogle Scholar
Shepard, R. N. (1974). Representation of structure in similarity data: Problems and prospects. Psychometrika, 39, 373–421.CrossRefGoogle Scholar
Shepard, R. N., Arabie, P. (1979). Additive clustering: Representation of similarities as combinations of discrete overlapping properties. Psychological Review, 86, 87–123.CrossRefGoogle Scholar
Shepard, R. N., Carroll, J. D. (1966). Parametric representation of nonlinear data structures. In Krishnaiah, P. R. (Eds.), Multivariate Analysis: Proceedings of an International Symposium, New York: Academic Press.Google Scholar
Sherman, C. R. (1972). Nonmetric multidimensional scaling: A Monte Carlo study of the basic parameters. Psychometrika, 37, 323–355.CrossRefGoogle Scholar
Spence, I. (1972). A Monte Carlo evaluation of three nonmetric multidimensional scaling algorithms. Psychometrika, 37, 461–486.CrossRefGoogle Scholar
Spence, I., Domoney, D. W. (1974). Single subject incomplete designs for nonmetric multidimensional scaling. Psychometrika, 39, 469–490.CrossRefGoogle Scholar
Stenson, H. H., Knoll, R. L. (1969). Goodness of fit for random rankings in Kruskal's nonmetric scaling procedure. Psychological Bulletin, 71, 122–126.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. (1952). Multidimensional scaling: I. Theory and method. Psychometrika, 17, 401–419.CrossRefGoogle Scholar
Torgerson, W. S. (1958). Theory and methods of scaling, New York: Wiley.Google Scholar
Torgerson, W. S. (1965). Multidimensional scaling of similarity. Psychometrika, 30, 379–393.CrossRefGoogle ScholarPubMed
Torgerson, W. S. (1968). Multidimensional representation of similarity structures. In Katz, M. M., Cole, J. O., Barton, W. E. (Eds.), The Role and Methodology of Classification in Psychiatry and Psychopathology, Washington, DC: U.S. Government Printing Office.Google Scholar
Torgerson, W. S. (1975, August). Types versus clusters. Paper presented at the U.S.—Japan Seminar on Theory, Methods and Applications of Multidimensional Scaling and Related Techniques, San Diego, CA.Google Scholar
Torgerson, W. S. (1983). The ideal type model. In Wainer, H., Messick, S. (Eds.), Principals of Modern Psychological Measurement, Hillsdale, NJ: Lawrence Erlbaum.Google Scholar
Torgerson, W. S., & Satalich, T. A. (1980, May). Hyperspherical and hypercylindrical multidimensional scaling: The ideal type model. Paper presented at the spring meeting of the Psychometric Society, Iowa City.Google Scholar
Tucker, L. R. (1972). Relations between multidimensional scaling and three-mode factor analysis. Psychometrika, 37, 3–27.CrossRefGoogle Scholar
Tucker, L. R., Messick, S. (1963). An individual differences model for multidimensional scaling. Psychometrika, 28, 333–367.CrossRefGoogle Scholar
Wagenaar, W. A., Padmos, P. (1971). Quantitative interpretation of stress in Kruskal's multidimensional scaling technique. British Journal of Mathematical and Statistical Psychology, 24, 101–110.CrossRefGoogle Scholar
Young, F. W. (1970). Nonmetric multidimensional scaling: Recovery of metric information. Psychometrika, 35, 455–473.CrossRefGoogle Scholar
Young, F. W., Torgerson, W. S. (1967). TORSCA, a Fortran IV program for nonmetric multidimensional scaling. Behavioral Science, 13, 343–344.CrossRefGoogle Scholar