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Determinantal Methods in Latent Class Analysis

Published online by Cambridge University Press:  01 January 2025

Albert Madansky
Albert Madansky*
Affiliation:
The Rand Corporation
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Abstract

Some extensions of the existing determinantal methods for solving the accounting equations in latent class analysis are presented. These extensions cover more cases than previous methods, give rise to new sufficient conditions for identifiability of the latent class model, and give insight into the necessity of various sufficient conditions for identifiability. These implications to the identifiability problem are discussed.

Type
Original Paper
Information
Psychometrika , Volume 25 , Issue 2 , June 1960 , pp. 183 - 198
Copyright
Copyright © 1960 The Psychometric Society

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Footnotes

*

This work, part of a doctoral dissertation submitted to the Department of Statistics of the University of Chicago, was made possible by The RAND Corporation and by a grant to the Department of Statistics of the University of Chicago by the Rockefeller Foundation. I gratefully acknowledge the comments of T. W. Anderson, W. H. Kruskal, and D. L. Wallace and especially the comments of L. A. Goodman on this work.

References

Anderson, T. W. On estimation of parameters in latent structure analysis. Psychometrika, 1954, 19, 1–10.CrossRefGoogle Scholar
Gibson, W. A. An extension of Anderson's solution for the latent structure equations. Psychometrika, 1955, 20, 69–73.CrossRefGoogle Scholar
Koopmans, T. C. Identification problems in latent structure analysis. Cowles Commission Discussion Paper: Statistics No. 360, 1951. (Mimeo.).Google Scholar
Lazarsfeld, P. F. Some new results and problems in latent structure analysis. Columbia Univ., 1956. (Mimeo.).Google Scholar
Lazarsfeld, P. F. and Dudman, J. The general solution of the latent class case. In “Mathematical developments in latent structure analysis.” The RAND Corp., Res. memo. RM-455, Part II, 1951.Google Scholar
Madansky, A. Determinantal methods in latent class analysis. The RAND Corp., Paper P-1538, 1958.Google Scholar
McHugh, R. B. Efficient estimation and local identification in latent class analysis. Psychometrika, 1956, 21, 331–347.CrossRefGoogle Scholar