Hostname: page-component-7b7567c8c-fvjsw Total loading time: 0 Render date: 2026-11-14T05:02:37.824Z Has data issue: false hasContentIssue false
  • English
  • Français

On a Metric, Unidimensional Unfolding Model for Attitudinal and Developmental Data

Published online by Cambridge University Press:  01 January 2025

Mark L. Davison
Mark L. Davison*
Affiliation:
University of Minnesota
*
Requests for reprints should be sent to Mark L. Davison, Department of Social, Psychological, and Philosophical Foundations of Education, 330 Burton Hall, University of Minnesota, Minneapolis, Minnesota.
Get accessRights & Permissions [Opens in a new window]

Abstract

If stimulus responses are linearly related to squared distances between stimulus scale values and person scores along a latent continuum, (a) the stimulus × stimulus correlation matrix will display a simplex-like pattern, (b) the signs of first-order partial correlations can be specified in an empirically testable manner, and (c) the variables will have a semicircular, two-factor structure. Along the semicircle, variables will be ordered by their positions on the latent dimension. The above results suggest procedures for examining the appropriateness of the model and procedures for ordering the stimuli. Applications to developmental and attitudinal data are discussed.

Keywords

factor analysisattitudespreferencesutility theorypersonality developmentpsychological scaling

Information

Type
Original Paper
Information
Psychometrika , Volume 42 , Issue 4 , December 1977, pp. 523 - 548
Copyright
Copyright © 1977 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 by a grant from the Graduate School of the University of Minnesota to the author and by a grant from the U. S. Public Health Service (Grant No. 1-R01-MH27861-01) to Dr. James Rest, Principal Investigator.

References

Reference Notes

Rest, J. Manual for the Defining Issues Test, 1974, Minneapolis, Minnesota: University of Minnesota.Google Scholar
Kohlberg, L. The development of modes of moral thinking and choice in the years ten to sixteen. Unpublished doctoral dissertation, University of Chicago, 1958.Google Scholar

References

Coombs, C. H. Psychological scaling without a unit of measurement. Psychological Review, 1950, 57, 145–158.CrossRefGoogle ScholarPubMed
Coombs, C. H. A theory of data, 1964, New York: Wiley.Google Scholar
Coombs, C. H. & Kao, R. C. On a connection between factor analysis and multidimensional unfolding. Psychometrika, 1960, 25, 219–231.CrossRefGoogle Scholar
Coombs, C. H. & Smith, J. E. K. On the detection of structure in attitude and developmental processes. Psychological Review, 1973, 80, 337–351.CrossRefGoogle Scholar
Guttman, L. A new approach to factor analysis: The radex. In Lazarsfeld, P. F.(Eds.), Mathematical Thinking in the Social Sciences, 1954, Glencoe, Ill.: Free Press.Google Scholar
Guttman, L. Some necessary conditions for common-factor analysis. Psychometrika, 1954, 19, 149–162.CrossRefGoogle Scholar
Hovland, C. I. & Sherif, M. Judgmental phenomena and scales of attitude measurement: Item displacement in Thurstone scales. Journal of Abnormal and Social Psychology, 1951, 46, 424–437.CrossRefGoogle Scholar
Hubert, L. Problems of seriation using a subject by item response matrix. Psychological Bulletin, 1974, 81, 976–983.CrossRefGoogle Scholar
Kohlberg, L. Stage and sequence: The cognitive-developmental approach to socialization. In Goslin, B. A.(Eds.), Handbook of socialization theory and research. San Francisco: Rand McNally. 1969, 347–380.Google Scholar
Kurtines, W. & Greif, E. B. The development of moral thought: Review and evaluation of Kohlberg's approach. Psychological Bulletin, 1974, 81, 453–470.CrossRefGoogle ScholarPubMed
Loevinger, J. The meaning and measurement of ego development. American Psychologist, 1966, 21, 195–206.CrossRefGoogle Scholar
Loevinger, J. Ego development, 1976, Washington, D. C.: Jossey-Bass.Google Scholar
Montanelli, R. G. & Humphreys, L. G. Latent roots of random data correlation matrices with squared multiple correlations on the diagonal: A monte carlo study. Psychometrika, 1976, 41, 341–348.CrossRefGoogle Scholar
Ramsey, J. O. Some statistical considerations in multidimensional scaling. Psychometrika, 1969, 34, 167–182.CrossRefGoogle Scholar
Rest, J. R., Cooper, D., Coder, R., Masanz, J. & Anderson, D. Judging the important issues in moral dilemmas—an objective test of development. Developmental Psychology, 1974, 10, 491–501.Google Scholar
Ross, J. & Cliff, N. A generalization of the interpoint distance model. Psychometrika, 1964, 29, 167–176.CrossRefGoogle Scholar
Schönemann, P. H. On metric multidimensional unfolding. Psychometrika, 1970, 35, 349–366.CrossRefGoogle Scholar
Thurstone, L. L. Attidues can be measured. American Journal of Sociology, 1928, 33, 529–554.CrossRefGoogle Scholar
Thurstone, L. L. The measurement of social attitudes. Journal of Abnormal and Social Psychology, 1931, 26, 249–269.CrossRefGoogle Scholar
Wohlwill, J. F. The study of behavioral development, 1973, New York: Academic Press.Google Scholar