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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 imposed on the parameter space of latent class models, through a design matrix, to reflect practitioners' diagnostic assumptions about how the observed responses depend on the respondent's latent traits. Though widely used in various fields, such restricted latent class models suffer from nonidentifiability due to the models' discrete nature and complex restricted structure. This work addresses the fundamental identifiability issue of restricted latent class models by developing a general framework for strict and partial identifiability of the model parameters. The developed identifiability conditions only depend on the design matrix and are easily checkable, which provides useful practical guidelines for designing statistically valid diagnostic tests. The new theoretical framework is applied to establish, for the first time, identifiability of several designs from cognitive diagnosis applications.
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