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

Author

Listed:
  • Xinyi Liu

    (London School of Economics and Political Science)

  • Gabriel Wallin

    (London School of Economics and Political Science
    Umeå University)

  • Yunxiao Chen

    (London School of Economics and Political Science)

  • Irini Moustaki

    (London School of Economics and Political Science)

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 $$L^p$$ L p loss functions $$(0

Suggested Citation

  • Xinyi Liu & Gabriel Wallin & Yunxiao Chen & Irini Moustaki, 2023. "Rotation to Sparse Loadings Using $$L^p$$ L p Losses and Related Inference Problems," Psychometrika, Springer;The Psychometric Society, vol. 88(2), pages 527-553, June.
    • Handle: RePEc:spr:psycho:v:88:y:2023:i:2:d:10.1007_s11336-023-09911-y
    DOI: 10.1007/s11336-023-09911-y
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    References listed on IDEAS

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    1. Y Chen & X Li, 2022. "Determining the number of factors in high-dimensional generalized latent factor models [Eigenvalue ratio test for the number of factors]," Biometrika, Biometrika Trust, vol. 109(3), pages 769-782.
    2. Henry Kaiser, 1958. "The varimax criterion for analytic rotation in factor analysis," Psychometrika, Springer;The Psychometric Society, vol. 23(3), pages 187-200, September.
    3. Jin, Shaobo & Moustaki, Irini & Yang-Wallentin, Fan, 2018. "Approximated penalized maximum likelihood for exploratory factor analysis: an orthogonal case," LSE Research Online Documents on Economics 88118, London School of Economics and Political Science, LSE Library.
    4. Robert Jennrich, 2002. "A simple general method for oblique rotation," Psychometrika, Springer;The Psychometric Society, vol. 67(1), pages 7-19, March.
    5. Haoran Zhang & Yunxiao Chen & Xiaoou Li, 2020. "A Note on Exploratory Item Factor Analysis by Singular Value Decomposition," Psychometrika, Springer;The Psychometric Society, vol. 85(2), pages 358-372, June.
    6. Elena Geminiani & Giampiero Marra & Irini Moustaki, 2021. "Single- and Multiple-Group Penalized Factor Analysis: A Trust-Region Algorithm Approach with Integrated Automatic Multiple Tuning Parameter Selection," Psychometrika, Springer;The Psychometric Society, vol. 86(1), pages 65-95, March.
    7. Shaobo Jin & Irini Moustaki & Fan Yang-Wallentin, 2018. "Approximated Penalized Maximum Likelihood for Exploratory Factor Analysis: An Orthogonal Case," Psychometrika, Springer;The Psychometric Society, vol. 83(3), pages 628-649, September.
    8. Nickolay Trendafilov, 2014. "From simple structure to sparse components: a review," Computational Statistics, Springer, vol. 29(3), pages 431-454, June.
    9. Geminiani, Elena & Marra, Giampiero & Moustaki, Irini, 2021. "Single and multiple-group penalized factor analysis: a trust-region algorithm approach with integrated automatic multiple tuning parameter selection," LSE Research Online Documents on Economics 108873, London School of Economics and Political Science, LSE Library.
    10. Chen, Yunxiao & Li, Xiaoou, 2022. "Determining the number of factors in high-dimensional generalized latent factor models," LSE Research Online Documents on Economics 111574, London School of Economics and Political Science, LSE Library.
    11. Mazumder, Rahul & Friedman, Jerome H. & Hastie, Trevor, 2011. "SparseNet: Coordinate Descent With Nonconvex Penalties," Journal of the American Statistical Association, American Statistical Association, vol. 106(495), pages 1125-1138.
    12. Vaart,A. W. van der, 2000. "Asymptotic Statistics," Cambridge Books, Cambridge University Press, number 9780521784504.
    13. Robert Jennrich, 2006. "Rotation to Simple Loadings Using Component Loss Functions: The Oblique Case," Psychometrika, Springer;The Psychometric Society, vol. 71(1), pages 173-191, March.
    14. Karl Jöreskog & Arthur Goldberger, 1972. "Factor analysis by generalized least squares," Psychometrika, Springer;The Psychometric Society, vol. 37(3), pages 243-260, September.
    15. R. Jennrich & P. Sampson, 1966. "Rotation for simple loadings," Psychometrika, Springer;The Psychometric Society, vol. 31(3), pages 313-323, September.
    16. Robert Jennrich, 2004. "Rotation to simple loadings using component loss functions: The orthogonal case," Psychometrika, Springer;The Psychometric Society, vol. 69(2), pages 257-273, June.
    17. Machado, José A.F., 1993. "Robust Model Selection and M-Estimation," Econometric Theory, Cambridge University Press, vol. 9(3), pages 478-493, June.
    18. Zhang, Haoran & Chen, Yunxiao & Li, Xiaoou, 2020. "A note on exploratory item factor analysis by singular value decomposition," LSE Research Online Documents on Economics 104166, London School of Economics and Political Science, LSE Library.
    19. Robert Jennrich, 1973. "Standard errors for obliquely rotated factor loadings," Psychometrika, Springer;The Psychometric Society, vol. 38(4), pages 593-604, December.
    20. Henk Kiers, 1994. "Simplimax: Oblique rotation to an optimal target with simple structure," Psychometrika, Springer;The Psychometric Society, vol. 59(4), pages 567-579, December.
    21. Yunxiao Chen & Xiaoou Li & Siliang Zhang, 2019. "Joint Maximum Likelihood Estimation for High-Dimensional Exploratory Item Factor Analysis," Psychometrika, Springer;The Psychometric Society, vol. 84(1), pages 124-146, March.
    22. Claude Archer & Robert Jennrich, 1973. "Standard errors for rotated factor loadings," Psychometrika, Springer;The Psychometric Society, vol. 38(4), pages 581-592, December.
    23. Yunxiao Chen & Xiaoou Li & Siliang Zhang, 2020. "Structured Latent Factor Analysis for Large-scale Data: Identifiability, Estimability, and Their Implications," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 115(532), pages 1756-1770, December.
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