Open Access
August 2020 Partial identifiability of restricted latent class models
Yuqi Gu, Gongjun Xu
Ann. Statist. 48(4): 2082-2107 (August 2020). DOI: 10.1214/19-AOS1878


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.


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Yuqi Gu. Gongjun Xu. "Partial identifiability of restricted latent class models." Ann. Statist. 48 (4) 2082 - 2107, August 2020.


Received: 1 March 2018; Revised: 1 May 2019; Published: August 2020
First available in Project Euclid: 14 August 2020

MathSciNet: MR4134787
Digital Object Identifier: 10.1214/19-AOS1878

Primary: 62E10 , 62P15

Keywords: $Q$-matrix , cognitive diagnosis , Identifiability , restricted latent class models

Rights: Copyright © 2020 Institute of Mathematical Statistics

Vol.48 • No. 4 • August 2020
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