Latent class models have wide applications in social and biological sciences. 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 respondents' 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. Furthermore, the new theoretical framework is applied to establish, for the first time, identifiability of several designs from cognitive diagnosis applications.

中文翻译：

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受限潜在类模型的部分可识别性

潜在类模型在社会科学和生物科学中具有广泛的应用。在许多应用中，通过设计矩阵对潜在类模型的参数空间施加预先指定的限制，以反映从业者关于观察到的响应如何取决于受访者的潜在特征的诊断假设。尽管广泛应用于各个领域，但由于模型的离散性和复杂的受限结构，这种受限的潜在类模型存在不可识别性。这项工作通过为模型参数的严格和部分可识别性开发一个通用框架，解决了受限潜在类模型的基本可识别性问题。开发的可识别性条件仅取决于设计矩阵，并且易于检查，它为设计统计上有效的诊断测试提供了有用的实用指南。此外，新的理论框架首次用于从认知诊断应用中建立几种设计的可识别性。