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Abstract:
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Latent class models have wide applications in social and biological sciences, which assume that the observed responses can be explained by some not directly measurable discrete latent attributes. In many applications, pre-specified restrictions are often imposed on the parameter space of the latent class models, through a design matrix, to reflect practitioners' diagnostic assumptions about how the observed responses depend on the respondent's latent traits. Such restricted latent class models, though widely used in cognitive diagnosis assessment, have been known by psychometricians and statisticians to suffer from the nonidentifiability issue due to the models' discrete nature and complex restricted structure. This talk considers the identifiability issues of the restricted latent class models and addresses several open questions in the literature by developing a general framework for the identifiability of the model parameters. The theoretical results are applied to establish for the first time the identifiability of several examples from cognitive diagnosis applications.
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