IDEAS home Printed from https://ideas.repec.org/a/eee/csdana/v54y2010i12p3020-3032.html
   My bibliography  Save this article

Robust estimation of constrained covariance matrices for confirmatory factor analysis

Author

Listed:
  • Dupuis Lozeron, E.
  • Victoria-Feser, M.P.

Abstract

Confirmatory factor analysis (CFA) is a data analysis procedure that is widely used in social and behavioral sciences in general and other applied sciences that deal with large quantities of data (variables). The classical estimator (and inference) procedures are based either on the maximum likelihood (ML) or generalized least squares (GLS) approaches which are known to be nonrobust to departures from the multivariate normal assumption underlying CFA. A natural robust estimator is obtained by first estimating the (mean and) covariance matrix of the manifest variables and then "plug-in" this statistic into the ML or GLS estimating equations. This two-stage method however does not fully take into account the covariance structure implied by the CFA model. An S-estimator for the parameters of the CFA model that is computed directly from the data is proposed instead and the corresponding estimating equations and an iterative procedure are derived. It is also shown that the two estimators have different asymptotic properties. A simulation study compares the finite sample properties of both estimators showing that the proposed direct estimator is more stable (smaller MSE) than the two-stage estimator.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:csdana:v:54:y:2010:i:12:p:3020-3032
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167-9473(09)00308-9
    Download Restriction: Full text for ScienceDirect subscribers only.
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Copt, Samuel & Victoria-Feser, Maria-Pia, 2006. "High-Breakdown Inference for Mixed Linear Models," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 292-300, March.
    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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Stephane Heritier & Maria-Pia Victoria-Feser, 2018. "Discussion of “The power of monitoring: how to make the most of a contaminated multivariate sample” by Andrea Cerioli, Marco Riani, Anthony C. Atkinson and Aldo Corbellini," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 27(4), pages 595-602, December.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. 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.
    2. Koller, Manuel, 2016. "robustlmm: An R Package for Robust Estimation of Linear Mixed-Effects Models," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 75(i06).
    3. 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.
    4. Osorio, Felipe & Paula, Gilberto A. & Galea, Manuel, 2007. "Assessment of local influence in elliptical linear models with longitudinal structure," Computational Statistics & Data Analysis, Elsevier, vol. 51(9), pages 4354-4368, May.
    5. Angela Montanari & Cinzia Viroli, 2010. "A skew-normal factor model for the analysis of student satisfaction towards university courses," Journal of Applied Statistics, Taylor & Francis Journals, vol. 37(3), pages 473-487.
    6. 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.
    7. Ruiz-Gazen, Anne & Lopuhaä, Henrik Paul & Gares, Valérie, 2022. "S-estimation in Linear Models with Structured Covariance Matrices," TSE Working Papers 22-1343, Toulouse School of Economics (TSE).
    8. Deliang Dai, 2020. "Mahalanobis Distances on Factor Model Based Estimation," Econometrics, MDPI, vol. 8(1), pages 1-11, March.
    9. Yu, Dalei & Ding, Chang & He, Na & Wang, Ruiwu & Zhou, Xiaohua & Shi, Lei, 2019. "Robust estimation and confidence interval in meta-regression models," Computational Statistics & Data Analysis, Elsevier, vol. 129(C), pages 93-118.
    10. 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.
    11. Chen, Yunxiao & Lu, Yan & Moustaki, Irini, 2022. "Detection of two-way outliers in multivariate data and application to cheating detection in educational tests," LSE Research Online Documents on Economics 112499, London School of Economics and Political Science, LSE Library.
    12. Yi-Hao Kao & Benjamin Van Roy, 2014. "Directed Principal Component Analysis," Operations Research, INFORMS, vol. 62(4), pages 957-972, August.
    13. 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.
    14. 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.
    15. Stephane Heritier & Maria-Pia Victoria-Feser, 2018. "Discussion of “The power of monitoring: how to make the most of a contaminated multivariate sample” by Andrea Cerioli, Marco Riani, Anthony C. Atkinson and Aldo Corbellini," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 27(4), pages 595-602, December.
    16. Christmann, A. & Van Aelst, S., 2006. "Robust estimation of Cronbach's alpha," Journal of Multivariate Analysis, Elsevier, vol. 97(7), pages 1660-1674, August.
    17. Anthony C. Atkinson & Marco Riani & Andrea Cerioli, 2018. "Cluster detection and clustering with random start forward searches," Journal of Applied Statistics, Taylor & Francis Journals, vol. 45(5), pages 777-798, April.
    18. Alper Sinan & B. Barıs Alkan, 2015. "A useful approach to identify the multicollinearity in the presence of outliers," Journal of Applied Statistics, Taylor & Francis Journals, vol. 42(5), pages 986-993, May.
    19. Aleš Toman, 2014. "Robust confirmatory factor analysis based on the forward search algorithm," Statistical Papers, Springer, vol. 55(1), pages 233-252, February.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:csdana:v:54:y:2010:i:12:p:3020-3032. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/csda .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.