Identifiability of Latent Class Models with Covariates

Abstract

Latent class models with covariates are widely used for psychological, social, and educational research. Yet the fundamental identifiability issue of these models has not been fully addressed. Among the previous research on the identifiability of latent class models with covariates, Huang and Bandeen-Roche (2004, Psychometrika, 69:5-32) studied the local identifiability conditions. However, motivated by recent advances in the identifiability of the restricted latent class models, particularly Cognitive Diagnosis Models (CDMs), we show in this work that the conditions in Huang and Bandeen-Roche (2004) are only necessary but not sufficient to determine the local identifiability of the model parameters. To address the open identifiability issue for latent class models with covariates, this work establishes conditions to ensure the global identifiability of the model parameters in both strict and generic senses. Moreover, our results extend to the polytomous-response CDMs with covariates, which generalizes the existing identifiability results for CDMs.

References in corpus (6)

• Identifiability of parameters in latent structure models with many observed variables
• The Sufficient and Necessary Condition for the Identifiability and Estimability of the DINA Model
• On the Identifiability of Diagnostic Classification Models
• Identifiability of restricted latent class models with binary responses
• Partial Identifiability of Restricted Latent Class Models
• Sufficient and Necessary Conditions for the Identifiability of the $Q$-matrix

Cited by in corpus (3)

• A two-step estimator for multilevel latent class analysis with covariates
• A Tensor-EM Method for Large-Scale Latent Class Analysis with Binary Responses
• A Restricted Latent Class Model with Polytomous Attributes and Respondent-Level Covariates