Skip to main content
SpringerLink
Log in
Book cover

COMPSTAT pp 385–390Cite as

A robust version of principal factor analysis

  • Conference paper

Abstract

Our aim is to construct a factor analysis method that can resist the effect of outliers. 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. A new type of empirical influence function (EIF) which is very effective for detecting influential data is constructed. If the data set contains fewer cases than variables, we estimate the factor loadings and scores by a robust interlocking regression algorithm.

This is a preview of subscription content, log in via an institution.

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  • Croux, C., Filzmoser, P., Pison, G. and Rousseeuw, P.J. (1999). Fitting Factor Models by Robust Interlocking Regression. Submitted for publication.

    Google Scholar 

  • Croux, C. and Haesbroeck, G. (1999). Influence Function and Efficiency of the Minimum Covariance Determinant Scatter Matrix Estimator. Journal of Multivariate Analysis, 71, pp. 161–190.

    Article  MathSciNet  MATH  Google Scholar 

  • Gray, J.B. (1985). Graphics for Regression Diagnostics. In: American Statistical Association Proceedings of the Statistical Computing Section, pp. 102–107. Washington, D.C.: ASA.

    Google Scholar 

  • Johnson, R.A. and Wichern, D.W. (1998). Applied Multivariate Statistical Analysis. New Jersey: Prentice Hall.

    Google Scholar 

  • Kosfeld, R. (1996). Robust Exploratory Factor Analysis. Statistical Papers, 37, pp. 105–122.

    Article  MATH  Google Scholar 

  • Rousseeuw, P.J. (1985). Multivariate Estimation with High Breakdown Point. In: Mathematical Statistics and Applications, Vol. B,pp. 283–297. Dordrecht: Reidel.

    Chapter  Google Scholar 

  • Rousseeuw, P.J. and Van Driessen, K. (1999). A Fast Algorithm for the Minimum Covariance Determinant Estimator.Technometrics 41, pp. 212–223.

    Article  Google Scholar 

  • Tanaka, Y. and Odaka, Y. (1989). Influential Observations in Principal Factor Analysis. Psychometrika 54, pp. 475–485.

    MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics and Computer Science, Universitaire Instelling Antwerpen, Universiteitsplein 1, B-2610, Antwerpen, Belgium

    G. Pison & P. J. Rousseeuw

  2. Department of Statistics and Probability Theory, Vienna University of Technology, Wiedner Hauptstrasse 8-10, A-1040, Vienna, Austria

    P. Filzmoser

  3. ECARE and Institut de Statistique, Université Libre de Bruxelles, CP-139, Avenue Roosevelt 50, B-1050, Bruxelles, Belgium

    C. Croux

Authors
  1. G. Pison
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. P. J. Rousseeuw
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. P. Filzmoser
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. C. Croux
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Department of Statistical Methods, Statistics Netherlands, P.O. Box 4000, 2270 JM, Voorburg, The Netherlands

    Jelke G. Bethlehem

  2. Faculty of Social Sciences, Department of Methodology and Statistics, Utrecht University, P.O. Box 80140, 3508 TC, Utrecht, The Netherlands

    Peter G. M. van der Heijden

Rights and permissions

Reprints and permissions

Copyright information

© 2000 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Pison, G., Rousseeuw, P.J., Filzmoser, P., Croux, C. (2000). A robust version of principal factor analysis. In: Bethlehem, J.G., van der Heijden, P.G.M. (eds) COMPSTAT. Physica, Heidelberg. https://doi.org/10.1007/978-3-642-57678-2_51

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-57678-2_51

  • Publisher Name: Physica, Heidelberg

  • Print ISBN: 978-3-7908-1326-5

  • Online ISBN: 978-3-642-57678-2

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation