Identifiability of Bifactor Models

TL;DR

This paper characterizes the conditions under which bifactor models in psychological and educational assessments are identifiable, ensuring valid parameter estimation and inference.

Contribution

It provides a comprehensive characterization of identifiability conditions for various bifactor models and offers practical tools for checking these conditions.

Findings

Identifiability conditions are fully characterized for linear and dichotomous bifactor models.

Simulation studies show estimation consistency depends on satisfying identifiability conditions.

Practical examples demonstrate how to check model identifiability through factor loadings.

Abstract

The bifactor model and its extensions are multidimensional latent variable models, under which each item measures up to one subdimension on top of the primary dimension(s). Despite their wide applications to educational and psychological assessments, this type of multidimensional latent variable models may suffer from non-identifiability, which can further lead to inconsistent parameter estimation and invalid inference. The current work provides a relatively complete characterization of identifiability for the linear and dichotomous bifactor models and the linear extended bifactor model with correlated subdimensions. In addition, similar results for the two-tier models are also developed. Illustrative examples are provided on checking model identifiability through inspecting the factor loading structure. Simulation studies are reported that examine estimation consistency when the identifiability conditions are/are not satisfied.