[RsR] Estimating robust distances in R (MVE vs. MCD)

[James Shaw]

I have been trying to estimate robust Mahalanobis distances in R for a
set of three regressors that includes one dummy variable.  Initially,
I tried generating robust MCD estimates and their associated VCE using
cob.rob.  However, when I did so I received the following error
message:  "Error in solve.default(cov, ...) :  Lapack routine dgesv:
system is exactly singular".  I believe that the MCD estimator
involves subsampling and that the parameter for the discrete variable
could not be identified in one of the subsamples due to insufficient
variance.  When using the minimum volume ellipsoid (MVE) estimator, I
did not experience any problems.  My code is given below.


x<-cbind(c0[,3], c0[,7], c0[,8])
rest<-cov.rob(x, method = "mve", nsamp = "exact", cor=FALSE)
xrd<-mahalanobis(x, rest$center, rest$cov, inverted=FALSE)
xrd<-xrd^.5
d0<-ifelse(xrd> 3.0575159,1,0)


Can anyone explain to me why the MVE estimator is able to accommodate
discrete variables, whereas the MCD estimator cannot do so?  I would
like to be certain that the method I used to estimate robust distances
is valid in light of the inclusion of a discrete variable in the
regressor set.

--
Jim


James W. Shaw, Ph.D., Pharm.D., M.P.H.
Assistant Professor
Department of Pharmacy Administration
College of Pharmacy
University of Illinois at Chicago
833 South Wood Street, M/C 871, Room 266
Chicago, IL 60612
Tel.: 312-355-5666
Fax: 312-996-0868
Mobile Tel.: 215-852-3045