Skip to main content
Log in

A probabilistic formulation and statistical analysis of guttman scaling

  • Published:
Psychometrika Aims and scope Submit manuscript


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.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others


  • Anderson, T. W. Some scaling models and estimation procedures in the latent class model. In U. Grenander (ed.),Probability and Statistics: the Harald Cramér volume. New York: John Wiley, 1959.

    Google Scholar 

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

    Google Scholar 

  • Festinger, L. The treatment of qualitative data by “scale analysis”.Psychological Bulletin, 1947,44, 149–161.

    Article  PubMed  Google Scholar 

  • Goodman, L. A. Simple statistical methods for scalogram analysis.Psychometrika, 1959,24, 29–43.

    Article  Google Scholar 

  • Guttman, L. On Festinger's evaluation of scale analysis.Psychological Bulletin, 1947,44, 451–465.

    Article  PubMed  Google Scholar 

  • Hayes, D. G. and Borgatta, E. F. An empirical comparison of restricted and general latent distance analysis.Psychometrika, 1954,19, 271–279.

    Article  Google Scholar 

  • Lazarsfeld, P. F. A conceptual introduction to latent structure analysis. In P. F. Lazarsfeld (ed.)Mathematical thinking in the social sciences. Glencoe, Illinois: The Free Press, 1954.

    Google Scholar 

  • Lazarsfeld, P. F. and Henry, N. W.Latent structure analysis. New York: Houghton Mifflin, 1968.

    Google Scholar 

  • Lord, F. E. A strong true-score theory, with applications.Psychometrika, 1965,30, 239–270.

    Article  PubMed  Google Scholar 

  • Miller, C. R. and Butler, E. W. A methodological evaluation of Srole's anomia scale.American Sociological Review, 1966,31, 400–406.

    Article  Google Scholar 

  • Rao, C. R.Linear statistical inference and its applications. New York: John Wiley, 1965.

    Google Scholar 

  • Torgerson, W. S.Theory and methods of scaling. New York: John Wiley, 1962.

    Google Scholar 

Download references

Author information

Authors and Affiliations


Rights and permissions

Reprints and permissions

About this article

Cite this article

Proctor, C.H. A probabilistic formulation and statistical analysis of guttman scaling. Psychometrika 35, 73–78 (1970).

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: