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A General Solution for the Latent Class Model of Latent Structure Analysis

Published online by Cambridge University Press:  01 January 2025

Bert F. Green Jr.
Bert F. Green Jr.*
Affiliation:
Educational Testing Service and Princeton University
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Abstract

For the point distribution model of Lazarsfeld's latent structure analysis, the general matrix equation is stated which relates the manifest data in the form of joint occurrence matrices to the latent parameters. The relationship of the item responses and these joint occurrence matrices is also indicated in matrix form. A general solution for the latent parameters is then presented, which is based on the notion of factoring two joint occurrence matrices. The solution is valid under certain conditions which will usually be fulfilled. The solution assumes that estimates are available for the elements in the joint occurrence matrices with recurring subscripts, analogous to item communality or reliability. Some alternative methods of obtaining these estimates are discussed. Finally a fictitious 3-class, 8-item example is presented in detail.

Type
Original Paper
Information
Psychometrika , Volume 16 , Issue 2 , June 1951 , pp. 151 - 166
Copyright
Copyright © 1951 The Psychometric Society

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Footnotes

*

Lazarsfeld, Paul. The logical and mathematical foundation of latent structure analysis. Stouffer, S., et al., Studies in social psychology in World War II. Vol. IV. Measurement and Prediotion, Princeton: Princeton University Press, 1950.

References

* In connection with a RAND project at Columbia University, Mr. W. A. Gibson has devised a graphical method of obtaining approximate solutions if certain configurational criteria are met, while Dr. Lazarsfeld and Mr. J. Dudman have solved special cases by the use of asymmetric determinants.

* Lazarsfeld, Paul, op. cit.