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A majorization algorithm for simultaneous parameter estimation in robust exploratory factor analysis

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  • Unkel, S.
  • Trendafilov, N.T.

Abstract

A new approach for fitting the exploratory factor analysis (EFA) model is considered. The EFA model is fitted directly to the data matrix by minimizing a weighted least squares (WLS) goodness-of-fit measure. The WLS fitting problem is solved by iteratively performing unweighted least squares fitting of the same model. A convergent reweighted least squares algorithm based on iterative majorization is developed. The influence of large residuals in the loss function is curbed using Huber's criterion. This procedure leads to robust EFA that can resist the effect of outliers in the data. Applications to real and simulated data illustrate the performance of the proposed approach.

Suggested Citation

  • Unkel, S. & Trendafilov, N.T., 2010. "A majorization algorithm for simultaneous parameter estimation in robust exploratory factor analysis," Computational Statistics & Data Analysis, Elsevier, vol. 54(12), pages 3348-3358, December.
    • Handle: RePEc:eee:csdana:v:54:y:2010:i:12:p:3348-3358
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    1. Groenen, P.J.F. & Giaquinto, P. & Kiers, H.A.L., 2003. "Weighted Majorization Algorithms for Weighted Least Squares Decomposition Models," Econometric Institute Research Papers EI 2003-09, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
    2. Pison, Greet & Rousseeuw, Peter J. & Filzmoser, Peter & Croux, Christophe, 2003. "Robust factor analysis," Journal of Multivariate Analysis, Elsevier, vol. 84(1), pages 145-172, January.
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    4. de Leeuw, Jan & Lange, Kenneth, 2009. "Sharp quadratic majorization in one dimension," Computational Statistics & Data Analysis, Elsevier, vol. 53(7), pages 2471-2484, May.
    5. Becker, Claudia & Gather, Ursula, 2001. "The largest nonidentifiable outlier: a comparison of multivariate simultaneous outlier identification rules," Computational Statistics & Data Analysis, Elsevier, vol. 36(1), pages 119-127, March.
    6. repec:ucp:bkecon:9780226316529 is not listed on IDEAS
    7. Henk Kiers, 1997. "Weighted least squares fitting using ordinary least squares algorithms," Psychometrika, Springer;The Psychometric Society, vol. 62(2), pages 251-266, June.
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    Cited by:

    1. repec:cup:judgdm:v:9:y:2014:i:5:p:500-509 is not listed on IDEAS
    2. Stegeman, Alwin, 2016. "A new method for simultaneous estimation of the factor model parameters, factor scores, and unique parts," Computational Statistics & Data Analysis, Elsevier, vol. 99(C), pages 189-203.
    3. Sundberg, Rolf & Feldmann, Uwe, 2016. "Exploratory factor analysis—Parameter estimation and scores prediction with high-dimensional data," Journal of Multivariate Analysis, Elsevier, vol. 148(C), pages 49-59.
    4. Lars Eldén & Nickolay Trendafilov, 2019. "Semi-sparse PCA," Psychometrika, Springer;The Psychometric Society, vol. 84(1), pages 164-185, March.
    5. Uno, Kohei & Satomura, Hironori & Adachi, Kohei, 2016. "Fixed factor analysis with clustered factor score constraint," Computational Statistics & Data Analysis, Elsevier, vol. 94(C), pages 265-274.
    6. Jushan Bai & Serena Ng, 2020. "Simpler Proofs for Approximate Factor Models of Large Dimensions," Papers 2008.00254, arXiv.org.
    7. Paolo Giordani & Roberto Rocci & Giuseppe Bove, 2020. "Factor Uniqueness of the Structural Parafac Model," Psychometrika, Springer;The Psychometric Society, vol. 85(3), pages 555-574, September.
    8. Kohei Uno & Kohei Adachi & Nickolay T. Trendafilov, 2019. "Clustered Common Factor Exploration in Factor Analysis," Psychometrika, Springer;The Psychometric Society, vol. 84(4), pages 1048-1067, December.
    9. Emilio Moyano-Díaz & Agustín Martínez-Molina & Fernando P. Ponce, 2014. "The price of gaining: maximization in decision-making, regret and life satisfaction," Judgment and Decision Making, Society for Judgment and Decision Making, vol. 9(5), pages 500-509, September.
    10. Kohei Adachi & Nickolay T. Trendafilov, 2018. "Some Mathematical Properties of the Matrix Decomposition Solution in Factor Analysis," Psychometrika, Springer;The Psychometric Society, vol. 83(2), pages 407-424, June.
    11. Liu, Litao & Cao, Zhi & Liu, Xiaojie & Shi, Lei & Cheng, Shengkui & Liu, Gang, 2020. "Oil security revisited: An assessment based on complex network analysis," Energy, Elsevier, vol. 194(C).

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