Hostname: page-component-745bb68f8f-l4dxg Total loading time: 0 Render date: 2025-01-07T19:02:28.876Z Has data issue: false hasContentIssue false

Extending Latent Class Solutions to Other Variables

Published online by Cambridge University Press:  01 January 2025

W. A. Gibson*
Affiliation:
Department of Army†

Abstract

A procedure is derived for estimating the latent parameters of items not initially included in a latent class solution, on the assumption that the relations between those additional items and the original ones are accounted for by the same latent structure. A chi-square test is proposed for evaluating the relatedness of the additional items to the latent structure. The extension is generalized to associate continuous outside variables with the original solution, and this is accompanied by the suggestion that a simple analysis of variance be used to assess the results. Finally, this latent structure extension is compared with the Dwyer extension of factor analysis.

Type
Original Paper
Copyright
Copyright © 1962 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.)

Footnotes

*

I am grateful to J. J. Mellinger for clarifying discussions of the statistical portions of this paper.

Opinions expressed herein are the author's, not the Army's.

References

Anderson, T. W. On estimation of parameters in latent structure analysis. Psychometrika, 1954, 19, 110.CrossRefGoogle Scholar
Dwyer, P. The determination of the factor loadings of a given test from the known factor loadings of other tests. Psychometrika, 1937, 2, 173178.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 Unpublished doctoral dissertation, Univ.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, 6973.CrossRefGoogle Scholar
Gibson, W. A. Multiple factors and latent structure. Unpublished manuscript.Google Scholar
Gibson, W. A. Three multivariate models: factor analysis, latent structure analysis, and latent profile analysis. Psychometrika, 1959, 24, 229252.CrossRefGoogle Scholar
Gibson, W. A. Positive manifold and latent structure. Unpublished manuscript.Google Scholar
Green, B. F. A general solution for the latent class model of latent structure analysis. Psychometrika, 1951, 16, 151166.CrossRefGoogle ScholarPubMed
Harman, H. H. Extensions of factorial solutions. Psychometrika, 1938, 3, 7584.CrossRefGoogle 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.Google 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.Google Scholar
McNemar, Q. Psychological statistics, New York: Wiley, 1955.Google Scholar
Madansky, A. Determinantal methods in latent class analysis. Psychometrika, 1960, 25, 183198.CrossRefGoogle Scholar