enetLTS: robust and sparse methods for high dimensional linear, binary, and multinomial regression

Abstract

enetLTS is an R package (R-Development-Core-Team, 2021) that provides a fully robust version of the elastic net estimator for high dimensional linear, binary, and multinomial regression. The elastic net penalization provides intrinsic variable selection and coefficient estimates for highly correlated variables, in particular for high dimensional low sample size data sets, and it has been extended to generalized linear regression models (Friedman et al., 2010). Combining these advantages with trimming outliers yields the robust solutions. The main idea of the algorithm is to search for outlier-free subsets on which the classical elastic net estimator can be applied. Outlier-free subsets are determined by trimming the penalized log-likelihood function for the considered regression model. The algorithm starts with 500 elemental subsets only for one combination of the elastic net parameters 𝛼 and 𝜆, and takes the warm start strategy for subsequent combinations in order to save the computation time. The final reweighting step is added to improve the statistical efficiency of the proposed estimators. From this point of view, the enet-LTS estimator can be seen as a trimmed version of the elastic net regression estimator for linear, binary, and multinomial regression (Friedman et al., 2010). Selecting model with the optimal tuning parameters is done via cross-validation, and various plots are available to illustrate model selection and to evaluate the final model estimates.