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.
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References
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.
Coombs, C. H.A theory of data. New York: John Wiley, 1964.
Festinger, L. The treatment of qualitative data by “scale analysis”.Psychological Bulletin, 1947,44, 149–161.
Goodman, L. A. Simple statistical methods for scalogram analysis.Psychometrika, 1959,24, 29–43.
Guttman, L. On Festinger's evaluation of scale analysis.Psychological Bulletin, 1947,44, 451–465.
Hayes, D. G. and Borgatta, E. F. An empirical comparison of restricted and general latent distance analysis.Psychometrika, 1954,19, 271–279.
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.
Lazarsfeld, P. F. and Henry, N. W.Latent structure analysis. New York: Houghton Mifflin, 1968.
Lord, F. E. A strong true-score theory, with applications.Psychometrika, 1965,30, 239–270.
Miller, C. R. and Butler, E. W. A methodological evaluation of Srole's anomia scale.American Sociological Review, 1966,31, 400–406.
Rao, C. R.Linear statistical inference and its applications. New York: John Wiley, 1965.
Torgerson, W. S.Theory and methods of scaling. New York: John Wiley, 1962.
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Proctor, C.H. A probabilistic formulation and statistical analysis of guttman scaling. Psychometrika 35, 73–78 (1970). https://doi.org/10.1007/BF02290594
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DOI: https://doi.org/10.1007/BF02290594