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

Green, Bert F., Jr.
Publication Year:
Report Number:
ETS Research Bulletin
Document Type:
Page Count:
Subject/Key Words:
Attitude Measures, Item Response Theory, Lazarsfeld, Paul, Mathematical Models, Matrices


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. A general solution of this equation for the latent parameters is 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 method is indicated for calculating a certain joint occurrence matrix needed in the solution.

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