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Robust factor analysis

Author

Listed:
  • Pison, Greet
  • Rousseeuw, Peter J.
  • Filzmoser, Peter
  • Croux, Christophe

Abstract

Our aim is to construct a factor analysis method that can resist the effect of outliers. For this we start with a highly robust initial covariance estimator, after which the factors can be obtained from maximum likelihood or from principal factor analysis (PFA). We find that PFA based on the minimum covariance determinant scatter matrix works well. We also derive the influence function of the PFA method based on either the classical scatter matrix or a robust matrix. These results are applied to the construction of a new type of empirical influence function (EIF), which is very effective for detecting influential data. To facilitate the interpretation, we compute a cutoff value for this EIF. Our findings are illustrated with several real data examples.

Suggested Citation

  • 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.
  • Handle: RePEc:eee:jmvana:v:84:y:2003:i:1:p:145-172
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    References listed on IDEAS

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    1. Croux, Christophe & Haesbroeck, Gentiane, 1999. "Influence Function and Efficiency of the Minimum Covariance Determinant Scatter Matrix Estimator," Journal of Multivariate Analysis, Elsevier, vol. 71(2), pages 161-190, November.
    2. Yutaka Tanaka & Yoshimasa Odaka, 1989. "Influential observations in principal factor analysis," Psychometrika, Springer;The Psychometric Society, vol. 54(3), pages 475-485, September.
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    Citations

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    Cited by:

    1. Gottard, Anna & Pacillo, Simona, 2010. "Robust concentration graph model selection," Computational Statistics & Data Analysis, Elsevier, vol. 54(12), pages 3070-3079, December.
    2. Hubert, Mia & Dierckx, Goedele & Vanpaemel, Dina, 2013. "Detecting influential data points for the Hill estimator in Pareto-type distributions," Computational Statistics & Data Analysis, Elsevier, vol. 65(C), pages 13-28.
    3. Eichengreen, Barry & Mody, Ashoka & Nedeljkovic, Milan & Sarno, Lucio, 2012. "How the Subprime Crisis went global: Evidence from bank credit default swap spreads," Journal of International Money and Finance, Elsevier, vol. 31(5), pages 1299-1318.
    4. Kim, Hyoung-Moon & Maadooliat, Mehdi & Arellano-Valle, Reinaldo B. & Genton, Marc G., 2016. "Skewed factor models using selection mechanisms," Journal of Multivariate Analysis, Elsevier, vol. 145(C), pages 162-177.
    5. Theodore Metaxas, 2012. "Urban Advantages and Disadvantages in Southeastern Europe: An Appreciation of Industrial Firms by Using Exploratory Factor Analysis," European Research Studies Journal, European Research Studies Journal, vol. 0(2), pages 81-104.
    6. METAXAS, Theodore, 2011. "Territorial Assets And Firms’ Competitiveness In Southern Europe: Industrial Vs Commercial Firms Using Exploratory Factor Analysis," Regional and Sectoral Economic Studies, Euro-American Association of Economic Development, vol. 11(1).
    7. Croux, Christophe & Joossens, Kristel, 2005. "Influence of observations on the misclassification probability in quadratic discriminant analysis," Journal of Multivariate Analysis, Elsevier, vol. 96(2), pages 384-403, October.
    8. repec:tou:journl:v:45:y:2017:p:131-158 is not listed on IDEAS
    9. Ella Roelant & Stefan Aelst & Gert Willems, 2009. "The minimum weighted covariance determinant estimator," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 70(2), pages 177-204, September.
    10. Christophe Croux & Peter Exterkate, 2011. "Sparse and Robust Factor Modelling," Tinbergen Institute Discussion Papers 11-122/4, Tinbergen Institute.
    11. Metaxas, Theodore & Duquenne, Marie Noelle, 2015. "Small and Medium Sized Firms’ Competitiveness and Territorial Characteristics by using a MLR approach," MPRA Paper 66848, University Library of Munich, Germany.
    12. Yang, Mingan & Dunson, David B. & Baird, Donna, 2010. "Semiparametric Bayes hierarchical models with mean and variance constraints," Computational Statistics & Data Analysis, Elsevier, vol. 54(9), pages 2172-2186, September.
    13. Aleš Toman, 2014. "Robust confirmatory factor analysis based on the forward search algorithm," Statistical Papers, Springer, vol. 55(1), pages 233-252, February.
    14. Verdonck, T. & Debruyne, M., 2011. "The influence of individual claims on the chain-ladder estimates: Analysis and diagnostic tool," Insurance: Mathematics and Economics, Elsevier, vol. 48(1), pages 85-98, January.
    15. Metaxas, Theodore & Kallioras, Dimitris, 2013. "Small and medium-sized firms' competitiveness and territorial characteristics/assets: The cases of Bari, Varna and Thessaloniki," MPRA Paper 52446, University Library of Munich, Germany.
    16. Cator, Eric A. & Lopuhaä, Hendrik P., 2010. "Asymptotic expansion of the minimum covariance determinant estimators," Journal of Multivariate Analysis, Elsevier, vol. 101(10), pages 2372-2388, November.
    17. Christmann, A. & Van Aelst, S., 2006. "Robust estimation of Cronbach's alpha," Journal of Multivariate Analysis, Elsevier, vol. 97(7), pages 1660-1674, August.
    18. Dupuis Lozeron, E. & Victoria-Feser, M.P., 2010. "Robust estimation of constrained covariance matrices for confirmatory factor analysis," Computational Statistics & Data Analysis, Elsevier, vol. 54(12), pages 3020-3032, December.

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