Abstract

We present a robust regression method for situations where there are continuous as well as binary regressors. The latter are often the result of encoding one or more categorical variables. In the first step we downweight leverage points by computing robust distances in the space of the continuous regressors. Then we perform a weighted least absolute values fit in function of the continuous as well as the binary regressors. Finally, the error scale is estimated robustly. We pay particular attention to the two-way model, in which the proposed estimator is compared with an algorithm that treats the continuous and the categorical variables alternatingly. An S-PLUS function for the proposed estimator is given, and used to analyze a recent data set from economics.

Keywords

Analysis of Covariance, Median Polish, Minimum Volume Ellipsoid Estimator, Outlier Detection, Robust Distance, Weighted Least Absolute Values.