Identifiability of Latent Class Models with Covariates

TL;DR

This paper investigates the fundamental identifiability of latent class models with covariates, establishing new conditions for global identifiability and extending results to polytomous-response cognitive diagnosis models.

Contribution

It provides necessary and sufficient conditions for global identifiability of latent class models with covariates, addressing gaps in previous local identifiability results and extending to more complex models.

Findings

Established conditions for global identifiability of latent class models with covariates.

Extended identifiability results to polytomous-response cognitive diagnosis models.

Clarified limitations of previous local identifiability conditions.

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.