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Rotation to sparse loadings using Lp losses and related inference problems

Liu, Xinyi Lin, Wallin, Gabriel, Chen, Yunxiao ORCID: 0000-0002-7215-2324 and Moustaki, Irini (2023) Rotation to sparse loadings using Lp losses and related inference problems. Psychometrika, 88 (2). pp. 527-553. ISSN 0033-3123

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Identification Number: 10.1007/s11336-023-09911-y


Researchers have widely used exploratory factor analysis (EFA) to learn the latent structure underlying multivariate data. Rotation and regularised estimation are two classes of methods in EFA that they often use to find interpretable loading matrices. In this paper, we propose a new family of oblique rotations based on component-wise L p loss functions (0 < p≤ 1) that is closely related to an L p regularised estimator. We develop model selection and post-selection inference procedures based on the proposed rotation method. When the true loading matrix is sparse, the proposed method tends to outperform traditional rotation and regularised estimation methods in terms of statistical accuracy and computational cost. Since the proposed loss functions are nonsmooth, we develop an iteratively reweighted gradient projection algorithm for solving the optimisation problem. We also develop theoretical results that establish the statistical consistency of the estimation, model selection, and post-selection inference. We evaluate the proposed method and compare it with regularised estimation and traditional rotation methods via simulation studies. We further illustrate it using an application to the Big Five personality assessment.

Item Type: Article
Additional Information: © 2023. The Author(s).
Divisions: Statistics
Subjects: H Social Sciences > HA Statistics
Date Deposited: 06 Mar 2023 15:06
Last Modified: 09 Jun 2024 19:18

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