Open Access
April 2017 Identifiability of restricted latent class models with binary responses
Gongjun Xu
Ann. Statist. 45(2): 675-707 (April 2017). DOI: 10.1214/16-AOS1464


Statistical latent class models are widely used in social and psychological researches, yet it is often difficult to establish the identifiability of the model parameters. In this paper, we consider the identifiability issue of a family of restricted latent class models, where the restriction structures are needed to reflect pre-specified assumptions on the related assessment. We establish the identifiability results in the strict sense and specify which types of restriction structure would give the identifiability of the model parameters. The results not only guarantee the validity of many of the popularly used models, but also provide a guideline for the related experimental design, where in the current applications the design is usually experience based and identifiability is not guaranteed. Theoretically, we develop a new technique to establish the identifiability result, which may be extended to other restricted latent class models.


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Gongjun Xu. "Identifiability of restricted latent class models with binary responses." Ann. Statist. 45 (2) 675 - 707, April 2017.


Received: 1 April 2015; Revised: 1 March 2016; Published: April 2017
First available in Project Euclid: 16 May 2017

zbMATH: 1371.62010
MathSciNet: MR3650397
Digital Object Identifier: 10.1214/16-AOS1464

Primary: 62E10

Keywords: $Q$-matrix , cognitive diagnosis models , Identifiability , Kruskal’s tensor decomposition , multivariate Bernoulli mixture , restricted latent class models

Rights: Copyright © 2017 Institute of Mathematical Statistics

Vol.45 • No. 2 • April 2017
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