Identifiability of restricted latent class models with binary responses

TL;DR

This paper investigates the conditions under which restricted latent class models with binary responses are identifiable, providing theoretical guarantees and design guidelines for social and psychological research applications.

Contribution

It establishes strict identifiability results for a family of restricted latent class models and introduces a new technique applicable to other similar models.

Findings

Identifiability depends on specific restriction structures.

Results guarantee validity of popular models.

Guidelines for experimental design to ensure identifiability.

Abstract

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.