Exact exploratory bi-factor analysis: a constraint-based optimisation approach

Qiao, Jiawei, Chen, Yunxiao ORCID: 0000-0002-7215-2324 and Ying, Zhiliang (2025) Exact exploratory bi-factor analysis: a constraint-based optimisation approach. Psychometrika. ISSN 0033-3123 (In Press)

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Abstract

Bi-factor analysis is a form of confirmatory factor analysis widely used in psychological and educational measurement. The use of a bi-factor model requires the specification of an explicit bi-factor structure on the relationship between the observed variables and the group factors. In practice, the bi-factor structure is sometimes unknown, in which case an exploratory form of bi-factor analysis is needed to find the bi-factor structure. Unfortunately, there are few methods for exploratory bi-factor analysis, with the exception of a rotation-based method proposed in Jennrich and Bentler (2011, 2012). However, the rotation-based method only finds approximate bi-factor structures, as it does not yield an exact bi-factor loading structure, even after applying hard thresholding. In this paper, we propose a constraint-based optimisation method that learns an exact bi-factor loading structure from data, overcoming the issue with the rotation-based method. The key to the proposed method is a mathematical characterisation of the bi-factor loading structure as a set of equality constraints, which allows us to formulate the exploratory bi-factor analysis problem as a constrained optimisation problem in a continuous domain and solve the optimisation problem with an augmented Lagrangian method. The power of the proposed method is shown via simulation studies and a real data example. Extending the proposed method to exploratory hierarchical factor analysis is also discussed. Code implementing the proposed method is open-source and publicly available at https://anonymous.4open.science/r/Bifactor-ALM-method-757D.

Item Type:	Article
Additional Information:	© 2025 The Author(s)
Divisions:	Statistics
Subjects:	B Philosophy. Psychology. Religion > BF Psychology H Social Sciences > HA Statistics
Date Deposited:	16 Apr 2025 15:48
Last Modified:	16 Apr 2025 15:48
URI:	http://eprints.lse.ac.uk/id/eprint/127955

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