PARTIAL IDENTIFIABILITY OF RESTRICTED LATENT CLASS MODELS

• 成果类型: Article
• 署名作者: Gu, Yuqi; Xu, Gongjun
• 署名单位: University of Michigan System; University of Michigan
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/19-AOS1878
• 发表日期: 2020
• 页码: 2082-2107
• 关键词: diagnostic classification models; Hidden Markov model; cognitive diagnosis; dina model; HIGHER-ORDER; rule-space; identification; FAMILY

摘要

Latent class models have wide applications in social and biological sciences. In many applications, prespecified restrictions are imposed on the parameter space of latent class models, through a design matrix, to reflect practitioners' assumptions about how the observed responses depend on subjects' latent traits. Though widely used in various fields, such restricted latent class models suffer from nonidentifiability due to their discreteness nature and complex structure of restrictions. 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. Under correct model specification, the developed identifiability conditions only depend on the design matrix and are easily checkable, which provide 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.