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Sparse Exploratory Factor Analysis

Author

Listed:
  • Nickolay T. Trendafilov

    (Open University)

  • Sara Fontanella

    (Imperial College London)

  • Kohei Adachi

    (Osaka University)

Abstract

Sparse principal component analysis is a very active research area in the last decade. It produces component loadings with many zero entries which facilitates their interpretation and helps avoid redundant variables. The classic factor analysis is another popular dimension reduction technique which shares similar interpretation problems and could greatly benefit from sparse solutions. Unfortunately, there are very few works considering sparse versions of the classic factor analysis. Our goal is to contribute further in this direction. We revisit the most popular procedures for exploratory factor analysis, maximum likelihood and least squares. Sparse factor loadings are obtained for them by, first, adopting a special reparameterization and, second, by introducing additional $$\ell _1$$ ℓ 1 -norm penalties into the standard factor analysis problems. As a result, we propose sparse versions of the major factor analysis procedures. We illustrate the developed algorithms on well-known psychometric problems. Our sparse solutions are critically compared to ones obtained by other existing methods.

Suggested Citation

  • Nickolay T. Trendafilov & Sara Fontanella & Kohei Adachi, 2017. "Sparse Exploratory Factor Analysis," Psychometrika, Springer;The Psychometric Society, vol. 82(3), pages 778-794, September.
    • Handle: RePEc:spr:psycho:v:82:y:2017:i:3:d:10.1007_s11336-017-9575-8
    DOI: 10.1007/s11336-017-9575-8
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    References listed on IDEAS

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    1. repec:ucp:bkecon:9780226316529 is not listed on IDEAS
    2. Clemens Hage & Martin Kleinsteuber, 2014. "Robust PCA and subspace tracking from incomplete observations using $$\ell _0$$ ℓ 0 -surrogates," Computational Statistics, Springer, vol. 29(3), pages 467-487, June.
    3. Nickolay Trendafilov & Kohei Adachi, 2015. "Sparse Versus Simple Structure Loadings," Psychometrika, Springer;The Psychometric Society, vol. 80(3), pages 776-790, September.
    4. Nickolay Trendafilov, 2014. "From simple structure to sparse components: a review," Computational Statistics, Springer, vol. 29(3), pages 431-454, June.
    5. Trendafilov, Nickolay T. & Jolliffe, Ian T., 2006. "Projected gradient approach to the numerical solution of the SCoTLASS," Computational Statistics & Data Analysis, Elsevier, vol. 50(1), pages 242-253, January.
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    Cited by:

    1. 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.
    2. 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.
    3. Lars Eldén & Nickolay Trendafilov, 2019. "Semi-sparse PCA," Psychometrika, Springer;The Psychometric Society, vol. 84(1), pages 164-185, March.
    4. 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.
    5. Yoav Bergner & Peter Halpin & Jill-Jênn Vie, 2022. "Multidimensional Item Response Theory in the Style of Collaborative Filtering," Psychometrika, Springer;The Psychometric Society, vol. 87(1), pages 266-288, March.
    6. M. Perrot‐Dockès & C. Lévy‐Leduc & L. Rajjou, 2022. "Estimation of large block structured covariance matrices: Application to ‘multi‐omic’ approaches to study seed quality," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 71(1), pages 119-147, January.
    7. Kim, Nam-Hwui & Browne, Ryan P., 2021. "In the pursuit of sparseness: A new rank-preserving penalty for a finite mixture of factor analyzers," Computational Statistics & Data Analysis, Elsevier, vol. 160(C).
    8. 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.
    9. Guangbao Guo & Chunjie Wei & Guoqi Qian, 2023. "Sparse online principal component analysis for parameter estimation in factor model," Computational Statistics, Springer, vol. 38(2), pages 1095-1116, June.

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