  For a robust leverage diagnostic in linear regression, Rousseeuw and van
Zomeren [1990] proposed using robust distance (Mahalanobis distance computed
using robust estimates of location and covariance). However, a design matrix X
that contains coded categorical predictor variables is often sufficiently
sparse that robust estimates of location and covariance cannot be computed.
Specifically, matrices formed by taking subsets of the rows of X are likely to
be singular, causing algorithms that rely on subsampling to fail. Following the
spirit of Maronna and Yohai [2000], we observe that extreme leverage points are
extreme in the continuous predictor variables. We therefore propose a robust
leverage diagnostic that combines a robust analysis of the continuous predictor
variables and the classical definition of leverage.
