Hostname: page-component-745bb68f8f-v2bm5 Total loading time: 0 Render date: 2025-01-07T18:38:36.787Z Has data issue: false hasContentIssue false
  • English
  • Français

A Probabilistic Formulation and Statistical Analysis of Guttman Scaling

Published online by Cambridge University Press:  01 January 2025

C. H. Proctor
C. H. Proctor*
Affiliation:
North Carolina State University
Get access Rights & Permissions [Opens in a new window]

Abstract

By proposing that the latent or true nature of subjects is identified with a limited number of response patterns (the Guttman scale patterns), the probability of an observed response pattern can be written as the sum of products of the probability of the true type multiplied by the chance of sufficient response error to cause the observed pattern to appear. This model contains the proportions of the true types as parameters plus some misclassification probabilities as parameters. Maximum likelihood methods are used to make estimates and test the fit for some examples.

Type
Original Paper
Information
Psychometrika , Volume 35 , Issue 1 , March 1970 , pp. 73 - 78
Copyright
Copyright © 1970 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

Anderson, T. W. Some scaling models and estimation procedures in the latent class model. In Grenander, U. (Eds.), Probability and Statistics: the Harald Cramér volume, 1959, New York: John Wiley.Google Scholar
Coombs, C. H. A theory of data, 1964, New York: John Wiley.Google Scholar
Festinger, L. The treatment of qualitative data by “scale analysis”. Psychological Bulletin, 1947, 44, 149–161.Google ScholarPubMed
Goodman, L. A. Simple statistical methods for scalogram analysis. Psychometrika, 1959, 24, 29–43.CrossRefGoogle Scholar
Guttman, L. On Festinger's evaluation of scale analysis. Psychological Bulletin, 1947, 44, 451–465.CrossRefGoogle ScholarPubMed
Hayes, D. G. and Borgatta, E. F. An empirical comparison of restricted and general latent distance analysis. Psychometrika, 1954, 19, 271–279.CrossRefGoogle Scholar
Lazarsfeld, P. F. A conceptual introduction to latent structure analysis. In Lazarsfeld, P. F. (Eds.), Mathematical thinking in the social sciences, 1954, Glencoe, Illinois: The Free Press.Google Scholar
Lazarsfeld, P. F. and Henry, N. W. Latent structure analysis, 1968, New York: Houghton Mifflin.Google Scholar
Lord, F. E. A strong true-score theory, with applications. Psychometrika, 1965, 30, 239–270.CrossRefGoogle Scholar
Miller, C. R. and Butler, E. W. A methodological evaluation of Srole's anomia scale. American Sociological Review, 1966, 31, 400–406.CrossRefGoogle Scholar
Rao, C. R. Linear statistical inference and its applications, 1965, New York: John Wiley.Google Scholar
Torgerson, W. S. Theory and methods of scaling, 1962, New York: John Wiley.Google Scholar