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Rotation to Sparse Loadings Using $$L^p$$ Losses and Related Inference Problems

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Rotation to Sparse Loadings Using $$L^p$$ Losses and Related Inference Problems. / Wallin, Gabriel.
In: Psychometrika, Vol. 88, No. 2, 30.06.2023, p. 527-553.

Research output: Contribution to Journal/Magazine › Journal article › peer-review

Harvard

Wallin, G 2023, 'Rotation to Sparse Loadings Using $$L^p$$ Losses and Related Inference Problems', Psychometrika, vol. 88, no. 2, pp. 527-553. https://doi.org/10.1007/s11336-023-09911-y

APA

Wallin, G. (2023). Rotation to Sparse Loadings Using $$L^p$$ Losses and Related Inference Problems. Psychometrika, 88(2), 527-553. https://doi.org/10.1007/s11336-023-09911-y

Vancouver

Wallin G. Rotation to Sparse Loadings Using $$L^p$$ Losses and Related Inference Problems. Psychometrika. 2023 Jun 30;88(2):527-553. Epub 2023 Mar 31. doi: 10.1007/s11336-023-09911-y

Author

Wallin, Gabriel. / Rotation to Sparse Loadings Using $$L^p$$ Losses and Related Inference Problems. In: Psychometrika. 2023 ; Vol. 88, No. 2. pp. 527-553.

Bibtex

@article{8703c9b54db743888d2e9c914f844590,
title = "Rotation to Sparse Loadings Using $$L^p$$ Losses and Related Inference Problems",
abstract = "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.",
author = "Gabriel Wallin",
year = "2023",
month = jun,
day = "30",
doi = "10.1007/s11336-023-09911-y",
language = "English",
volume = "88",
pages = "527--553",
journal = "Psychometrika",
issn = "0033-3123",
publisher = "Springer New York",
number = "2",

}

RIS

TY - JOUR

T1 - Rotation to Sparse Loadings Using $$L^p$$ Losses and Related Inference Problems

AU - Wallin, Gabriel

PY - 2023/6/30

Y1 - 2023/6/30

N2 - 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.

AB - 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.

U2 - 10.1007/s11336-023-09911-y

DO - 10.1007/s11336-023-09911-y

M3 - Journal article

C2 - 37002429

VL - 88

SP - 527

EP - 553

JO - Psychometrika

JF - Psychometrika

SN - 0033-3123

IS - 2

ER -