Hostname: page-component-89b8bd64d-z2ts4 Total loading time: 0 Render date: 2026-05-08T17:26:55.429Z Has data issue: false hasContentIssue false
  • English
  • Français

An Individual differences Model for Multidimensional Scaling

Published online by Cambridge University Press:  01 January 2025

Ledyard R Tucker  and
Samuel Messick
Ledyard R Tucker
Affiliation:
University of Illinois
Samuel Messick
Affiliation:
Educational Testing Service
Get access Rights & Permissions [Opens in a new window]

Abstract

A quantitative system is presented to permit the determination of separate multidimensional perceptual spaces for individuals having different viewpoints about stimulus interrelationships. The structure of individual differences in the perception of stimulus relationships is also determined to provide a framework for ascertaining the varieties of consistent individual viewpoints and their relationships with other variables.

Information

Type
Original Paper
Information
Psychometrika , Volume 28 , Issue 4 , December 1963 , pp. 333 - 367
Copyright
Copyright © 1963 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.)

Article purchase

Temporarily unavailable

Footnotes

*

This research was supported in part by the National Institute of Mental Health, United States Public Health Service, under Research Grants M-2878 and M-4186 to Educational Testing Service, in part by Educational Testing Service, and in part by the Office of Naval Research under Contract Nonr-1834(39) and the University of Illinois. The authors wish to thank Drs. Harold Gulliksen and Douglas N. Jackson for their helpful comments and Miss Henrietta Gallagher for supervising the computations. Portions of this paper were presented at the American Psychological Association meetings in Chicago, September 1960.

†

This paper was written while Dr. Messick was a Fellow at the Center for Advanced Study in the Behavioral Sciences.

References

Abelson, R. P. A technique and a model for multidimensional attitude scaling. Publ. opin. Quart., 1954, 18, 405–418.CrossRefGoogle Scholar
Abelson, R. P. and Sermat, V. Multidimensional scaling of facial expressions. J. exp. Psychol., 1962, 63, 546–554.CrossRefGoogle ScholarPubMed
Adams, E. and Messick, S. An axiomatic formulation and generalization of successive intervals scaling. Psychometrika, 1958, 23, 355–368.CrossRefGoogle Scholar
Attneave, F. Dimensions of similarity. Amer. J. Psychol., 1950, 63, 516–556.CrossRefGoogle ScholarPubMed
Bieri, J. and Blacker, E. The generality of cognitive complexity in the perception of people and inkblots. J. abnorm. soc. Psychol., 1956, 53, 112–117.CrossRefGoogle ScholarPubMed
Bock, R. D. The selection of judges for preference testing. Psychometrika, 1956, 21, 349–366.CrossRefGoogle Scholar
Cliff, N. Analytic rotation to a functional relationship. Psychometrika, 1962, 27, 283–295.CrossRefGoogle Scholar
Coombs, C. H. An application of a nonmetric model for multidimensional analysis of similarities. Psychol. Rep., 1958, 4, 511–518.CrossRefGoogle Scholar
Diederich, G. W., Messick, S. and Tucker, L. R. A general least squares solution for successive intervals. Psychometrika, 1957, 22, 159–173.CrossRefGoogle Scholar
Eckart, C. and Young, G. The approximation of one matrix by another of lower rank. Psychometrika, 1936, 1, 211–218.CrossRefGoogle Scholar
Ekman, G. Dimensions of color vision. J. Psychol., 1954, 38, 467–474.CrossRefGoogle Scholar
Gulliksen, H. Linear and multidimensional scaling. Psychometrika, 1961, 26, 9–25.CrossRefGoogle Scholar
Gulliksen, H. The structure of individual differences in optimality judgments. In Bryan, G. and Shelly, M. (Eds.), Human judgments and optimality, New York: Wiley, 1963.Google Scholar
Harman, H. H. Modern factor analysis, Chicago: Univ. Chicago Press, 1960.Google Scholar
Harvey, O. J., Hunt, D. E. and Schroder, H. M. Conceptual systems and personality organization, New York: Wiley, 1961.Google Scholar
Helm, C. A multidimensional ratio scaling analysis of perceived color relations. Princeton, N. J.: ONR Technical Report, Educational Testing Service, 1959.Google Scholar
Helm, C. and Tucker, L. R. Individual differences in the structure of color perception. Amer. J. Psychol., 1962, 75, 437–444.CrossRefGoogle ScholarPubMed
Holzinger, K. J. Factoring test scores and implications for the method of averages. Psychometrika, 1944, 9, 155–167.CrossRefGoogle Scholar
Horst, P. Matrix algebra for social scientists, New York: Holt, Rinehart, and Winston, 1963.Google Scholar
Hotelling, H. Analysis of a complex of statistical variables into principal components. J. educ. Psychol., 1933, 24, 417–441.CrossRefGoogle Scholar
Indow, T. and Kanazawa, K. Multidimensional mapping of Munsell colors varying in hue, chroma, and value. J. exp. Psychol., 1960, 59, 330–336.CrossRefGoogle ScholarPubMed
Indow, T. and Uchizono, T. Multidimensional mapping of Munsell colors varying in hue and chroma. J. exp. Psychol., 1960, 59, 321–329.CrossRefGoogle ScholarPubMed
Jackson, D. N. and Messick, S. Individual differences in social perception. Brit. J. soc. clin. Psychol., 1963 (in press).CrossRefGoogle Scholar
Jackson, D. N., Messick, S., Solley, C. M.. A multidimensional scaling approach to the perception of personality. J. Psychol., 1957, 44, 311–318.CrossRefGoogle Scholar
Klingberg, F. L.. Studies in measurement of the relations between sovereign states. Psychometrika, 1941, 6, 335–352.CrossRefGoogle Scholar
Messick, S.. The perception of social attitudes. J. abnorm. soc. Psychol., 1956, 52, 57–66.CrossRefGoogle ScholarPubMed
Messick, S.. Some recent theoretical developments in multidimensional scaling. Educ. psychol. Measmt, 1956, 16, 82–100.CrossRefGoogle Scholar
Messick, S.. An empirical evaluation of multidimensional successive intervals. Psychometrika, 1956, 21, 367–375.CrossRefGoogle Scholar
Messick, S.. Dimensions of social desirability. J. consult. Psychol., 1960, 24, 279–287.CrossRefGoogle Scholar
Messick, S.. The perceived structure of political relationships. Sociometry, 1961, 24, 270–278.CrossRefGoogle Scholar
Messick, S. and Abelson, R. P.. The additive constant problem in multidimensional scaling. Psychometrika, 1956, 21, 1–15.CrossRefGoogle Scholar
Messick, S. and Kogan, N. Differentiation and compartmentalization in objectsorting measures of categorizing style. Percept. mot. Skills, 1963, 16, 47–51.CrossRefGoogle ScholarPubMed
Morris, C. and Jones, L. V. Value scales and dimensions. J. abnorm. soc. Psychol., 1955, 51, 523–535.CrossRefGoogle ScholarPubMed
Morton, A. S. Similarity as a determinant of friendship: A multidimensional study. Princeton, N. J.: ONR Technical Report, Educational Testing Service, 1959.Google Scholar
Mosier, C. I. Determining a simple structure when loadings for certain tests are known. Psychometrika, 1939, 4, 149–162.CrossRefGoogle Scholar
Nunnally, J. The analysis of profile data. Psychol. Bull., 1962, 59, 311–319.CrossRefGoogle ScholarPubMed
Reeb, M. How people see jobs: A multidimensional analysis. Occupational Psychol., 1959, 33, 1–17.Google Scholar
Richardson, M. W. Multidimensional psychophysics. Psychol. Bull., 1938, 35, 659–660 (Abstract).Google Scholar
Scott, W. A. Cognitive complexity and cognitive flexibility. Sociometry, 1962, 25, 405–414.CrossRefGoogle Scholar
Shepard, R. N. Stimulus and response generalization: Tests of a model relating generalization to distance in psychological space. J. exp. Psychol., 1958, 55, 509–523.CrossRefGoogle Scholar
Shepard, R. N. Similarity of stimuli and metric properties of behavioral data. In Gulliksen, H. and Messick, S. (Eds.), Psychological scaling: Theory and applications. New York: Wiley, 1960, 33–43.Google Scholar
Shepard, R. N. The analysis of proximities: Multidimensional scaling with an unknown distance function: I. Psychometrika, 1962, 27, 125–140.CrossRefGoogle Scholar
Shepard, R. N. The analysis of proximities: Multidimensional scaling with an unknown distance function: II. Psychometrika, 1962, 27, 219–246.CrossRefGoogle Scholar
Slater, P. The analysis of personal preferences. Brit. J. statist. Psychol., 1960, 13, 119–135.CrossRefGoogle Scholar
Sloane, H., Gorlow, L. and Jackson, D. N. Cognitive styles in equivalence range. Percept. mot. Skills, 1963, 16, 389–404.CrossRefGoogle ScholarPubMed
Torgerson, W. S. A theoretical and empirical investigation of multidimensional scaling. Unpublished doctoral dissertation, Princeton Univ., 1951.CrossRefGoogle Scholar
Torgerson, W. S. Multidimensional scaling: I. Theory and method. Psychometrika, 1952, 17, 401–419.CrossRefGoogle Scholar
Torgerson, W. S. Theory and methods of scaling, New York: Wiley, 1958.Google Scholar
Tucker, L. R. Description of paired comparison preference judgments by a multi-dimensional vector model. Princeton, N. J.: Educational Testing Service, Res. Memo., 1955, 55–57.Google Scholar
Tucker, L R. Intra-individual and inter-individual multidimensionality. In Gulliksen, H. and Messick, S. (Eds.), Psychological scaling: Theory and applications. New York: Wiley, 1960, 155–167.Google Scholar
Tucker, L R. Systematic differences between individuals in perceptual judgments. In Bryan, G. and Shelly, M. (Eds.), Human judgments and optimality, New York: Wiley, 1963.Google Scholar
Young, G. and Householder, A. S. Discussion of a set of points in terms of their mutual distances. Psychometrika, 1938, 3, 19–22.CrossRefGoogle Scholar