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Three Multivariate Models: Factor Analysis, Latent Structure Analysis, and Latent Profile Analysis

Published online by Cambridge University Press:  01 January 2025

W. A. Gibson
W. A. Gibson*
Affiliation:
Personnel Research Branch, The Adjutant General's Office
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Abstract

The factor analysis model and Lazarsfeld's latent structure scheme for analyzing dichotomous attributes are derived to show how the latter model avoids three knotty problems in factor analysis: communality estimation, rotation, and curvilinearity. Then the latent structure model is generalized into latent profile analysis for the study of interrelations among quantitative measures. Four latent profile examples are presented and discussed in terms of their limitations and the problems of latent metric and dimensionality thereby raised. The possibility of treating higher order empirical relations in a manner paralleling their various uses in the latent structure model is indicated.

Information

Type
Original Paper
Information
Psychometrika , Volume 24 , Issue 3 , September 1959 , pp. 229 - 252
Copyright
Copyright © 1959 The Psychometric Society

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Footnotes

*

The latter model is anticipated in an earlier paper by Green [12].

†

The major portion of this paper was completed at the Center for Advanced Study in the Behavioral Sciences. The opinions expressed are those of the author and are not to be construed as reflecting official Department of the Army policy.

References

Anderson, T. W. On estimation of parameters in latent structure analysis. Psychometrika, 1954, 19, 1–10.CrossRefGoogle Scholar
Carroll, J. B. The effect of difficulty and chance success on correlations between items or between tests. Psychometrika, 1945, 10, 1–19.CrossRefGoogle Scholar
Davis, F. B. Fundamental factors of comprehension in reading. Psychometrika, 1944, 9, 185–197.CrossRefGoogle Scholar
Ferguson, G. A. The factorial interpretation of test difficulty. Psychometrika, 1941, 6, 323–329.CrossRefGoogle Scholar
Gibson, W. A. Applications of the mathematics of multiple-factor analysis to problems of latent structure analysis. In Lazarsfeld, P. F. et al., The use of mathematical models in the measurement of attitudes. Res. Memo. No. 455, Rand Corp., 1951.Google Scholar
Gibson, W. A. Applications of the mathematics of multiple-factor analysis to problems of latent structure analysis. Unpublished doctoral dissertation, Univ. Chicago, 1951.Google Scholar
Gibson, W. A. An extension of Anderson's solution for the latent structure equations. Psychometrika, 1955, 20, 69–73.CrossRefGoogle Scholar
Gibson, W. A. Multiple factors and latent structure. Unpublished manuscript.Google Scholar
Gibson, W. A. Nonlinear factor analysis, single factor case. Amer. Psychologist, 1955, 10, 438–438. (Abstract)Google Scholar
Gibson, W. A. Nonlinear factors in two dimensions. Amer. Psychologist, 1956, 11, 415–415. (Abstract)Google Scholar
Green, B. F. A general solution for the latent class model of latent structure analysis. Psychometrika, 1951, 16, 151–166.CrossRefGoogle ScholarPubMed
Green, B. F. Latent structure analysis and its relation to factor analysis. J. Amer. statist. Ass., 1952, 47, 71–76.CrossRefGoogle Scholar
Guilford, J. P. The difficulty of a test and its factor composition. Psychometrika, 1941, 6, 67–77.CrossRefGoogle Scholar
Lazarsfeld, P. F. The interpretation and computation of some latent structures. In Stouffer, S. A. et al., Measurement and prediction. Princeton: Princeton Univ. Press, 1950, 11–11.Google Scholar
Lazarsfeld, P. F. The logical and mathematical foundation of latent structure analysis. In Stouffer, S. A. et al., Measurement and prediction. Princeton: Princeton Univ. Press, 1950, 10–10.Google Scholar
Lazarsfeld, P. F. Some new results and problems in latent structure analysis. Unpublished manuscript.Google Scholar
Lazarsfeld, P. F., et al. The use of mathematical models in the measurement of attitudes. Res. Memo. No. 455, Rand Corp., 1951.Google Scholar
Thurstone, L. L. Multiple-factor analysis, Chicago: Univ. Chicago Press, 1947.Google Scholar
Thurstone, L. L. Note on a reanalysis of Davis' reading tests. Psychometrika, 1946, 11, 185–188.CrossRefGoogle Scholar
Wherry, R. J. and Gaylord, R. H. Factor pattern of test items and tests as a function of the correlation coefficient: content, difficulty, and constant error factors. Psychometrika, 1944, 9, 237–244.CrossRefGoogle Scholar