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.
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References
Anderson, T. W. On estimation of parameters in latent structure analysis.Psychometrika, 1954,19, 1–10.
Carroll, J. B. The effect of difficulty and chance success on correlations between items or between tests.Psychometrika, 1945,10, 1–19.
Davis, F. B. Fundamental factors of comprehension in reading.Psychometrika, 1944,9, 185–197.
Ferguson, G. A. The factorial interpretation of test difficulty.Psychometrika, 1941,6, 323–329.
Gibson, W. A. Applications of the mathematics of multiple-factor analysis to problems of latent structure analysis. In P. F. Lazarsfeld et al., The use of mathematical models in the measurement of attitudes. Res. Memo. No. 455, Rand Corp., 1951.
Gibson, W. A. Applications of the mathematics of multiple-factor analysis to problems of latent structure analysis. Unpublished doctoral dissertation, Univ. Chicago, 1951.
Gibson, W. A. An extension of Anderson's solution for the latent structure equations.Psychometrika, 1955,20, 69–73.
Gibson, W. A. Multiple factors and latent structure. Unpublished manuscript.
Gibson, W. A. Nonlinear factor analysis, single factor case.Amer. Psychologist, 1955,10, 438. (Abstract)
Gibson, W. A. Nonlinear factors in two dimensions.Amer. Psychologist, 1956,11, 415 (Abstract)
Green, B. F. A general solution for the latent class model of latent structure analysis.Psychometrika, 1951,16, 151–166.
Green, B. F. Latent structure analysis and its relation to factor analysis.J. Amer. statist. Ass., 1952,47, 71–76.
Guilford, J. P. The difficulty of a test and its factor composition.Psychometrika, 1941,6, 67–77.
Lazarsfeld, P. F. The interpretation and computation of some latent structures. In S. A. Stouffer et al.,Measurement and prediction. Princeton: Princeton Univ. Press, 1950. Ch. 11.
Lazarsfeld, P. F. The logical and mathematical foundation of latent structure analysis. In S. A. Stouffer et al.,Measurement and prediction. Princeton: Princeton Univ. Press, 1950. Ch. 10.
Lazarsfeld, P. F. Some new results and problems in latent structure analysis. Unpublished manuscript.
Lazarsfeld, P. F., et al. The use of mathematical models in the measurement of attitudes. Res. Memo. No. 455, Rand Corp., 1951.
Thurstone, L. L.Multiple-factor analysis. Chicago: Univ. Chicago Press, 1947.
Thurstone, L. L. Note on a reanalysis of Davis' reading tests.Psychometrika, 1946,11, 185–188.
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.
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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.
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Gibson, W.A. Three multivariate models: Factor analysis, latent structure analysis, and latent profile analysis. Psychometrika 24, 229–252 (1959). https://doi.org/10.1007/BF02289845
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DOI: https://doi.org/10.1007/BF02289845