A robust and sparse estimator for multinomial regression is proposed for
high dimensional data. Robustness of the estimator is achieved by trimming
the maximum likelihood function, and sparsity is obtained by the elastic net
penalty. In contrast to multi-group classifiers based on dimension reduction,
this model is very appealing in terms of interpretation, since one obtains
estimated coefficients individually for every group, and also the sparsity of
the coefficients is group specific.
Simulation studies underline the excellent performance in comparison to the
non-robust version of the multinomial regression estimator, and some real
data example reveal the usefulness of this robust estimator particularly in
terms of result interpretation and model diagnostics. The procedure has
been implemented in the R package enetLTS.
- 17/04/2023 2:30 pm