Fitting multiplicative models by robust alternating regressions

Authors:
C. Croux;P. Filzmoser;G. Pison;P. J. Rousseeuw
Affiliations:
Department of Applied Economics, K.U. Leuven, Naamsestraat 69, B-3000 Leuven, Belgium;Institute of Statistics and Probability Theory, Vienna University of Technology, Vienna, Austria. P.Filzmoser@tuwien.ac.at;Department of Mathematics and Computer Science, Universitaire Instelling Antwerpen, Belgium;Department of Mathematics and Computer Science, Universitaire Instelling Antwerpen, Belgium
Venue:
Statistics and Computing
Year:
2003

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Abstract

In this paper a robust approach for fitting multiplicative models is presented. Focus is on the factor analysis model, where we will estimate factor loadings and scores by a robust alternating regression algorithm. The approach is highly robust, and also works well when there are more variables than observations. The technique yields a robust biplot, depicting the interaction structure between individuals and variables. This biplot is not predetermined by outliers, which can be retrieved from the residual plot. Also provided is an accompanying robust R2-plot to determine the appropriate number of factors. The approach is illustrated by real and artificial examples and compared with factor analysis based on robust covariance matrix estimators. The same estimation technique can fit models with both additive and multiplicative effects (FANOVA models) to two-way tables, thereby extending the median polish technique.