Robust factor analysis

Authors:
Greet Pison;Peter J. Rousseeuw;Peter Filzmoser;Christophe Croux
Affiliations:
Department of Mathematics and Computer Science, Universitaire Instelling, Antwerpen, Universiteitsplein 1, B-2610 Wilrijk, Belgium;Department of Mathematics and Computer Science, Universitaire Instelling, Antwerpen, Universiteitsplein 1, B-2610 Wilrijk, Belgium;Department of Statistics, Probability Theory and Actuarial Mathematics, Vienna University of Technology, Wiedner Hauptstrasse 8-10, A-1040 Vienna, Austria;Department of Applied Economics, K. U. Leuven, Naamsestraat 69, B-3000 Leuven, Belgium
Venue:
Journal of Multivariate Analysis
Year:
2003

Citing 5
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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.