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Latent Class Analysis: A General Solution and an Empirical Evaluation

Green, Bert F., Jr.
Publication Year:
Report Number:
ETS Research Bulletin
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Subject/Key Words:
Chapin Living Room Scale, Latent Structure, Mathematical Models, Scaling


Latent Structure Analysis is here defined as a mathematical model for describing the interrelationships of items in a psychological test or questionnaire on the basis of which it is possible to make some inferences about hypothetical fundamental variables assumed to underlie the responses. It is also possible to consider the distribution of respondents on these underlying variables. This study was undertaken to attempt to develop a general procedure for applying a specific variant of the latent structure model, the latent class model, to data. The general models for latent structure analysis and latent class analysis are described in Chapters II and III. In order to test the adequacy of this general method, two experiments were conducted using hypothetical data. In each experiment, a hypothetical latent class structure was set up, and data generated from this structure by means of random numbers. This resulted in data which represented a random sample from a population with the specified structure. The general method for applying the model which had been developed was used with these data, and the derived structure compared with the hypothetical structure. The results of these experiments are reported in Chapter IV, "The Random Number Experiments". Finally, in Chapter V, "A Latent Class Analysis of the Chapin Living Room Scale", the model is applied to the Chapin Living Room Scale, a scale designed to measure socio- economic status. This example indicates the kind of conclusions which may be drawn on the basis of a latent class analysis. Conclusions include: 1) if a set of data exhibits a latent class structure, the procedures of Chapter III will give satisfactory approximations to the actual parameters. The iterative solution, the direct solution, and the approximate solution are all usable; 2) a decision as to which method to use in any actual situation may be made primarily on the basis of ease of computation, which may depend on the number of classes in the structure; 3) the latent class model does not fit the Chapin Living Room Scale as it stands, although the elimination of two items would allow a three class structure to fit the data fairly well; and 4) the three classes thus obtained would "appear to permit an ordering along a single dimension which may be called living room decor or socio-economic status..." (JGL)

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