Study on the performance of Robust LASSO in determining important variables data with outliers

Abstract

A variable selection method is required to deal with regression models with many variables, and LASSO has been the most widely used methodology.  However, as several authors have noted, LASSO is sensitive to outliers in the data.  For this reason, the Robust-LASSO approach was introduced by applying some weighting schemes for each sample in the data.  This research presented a comparative study of the three weighting schemes in Robust LASSO, namely Huber-LASSO, Tukey-LASSO, and Welsch-LASSO.  The study did a rich simulation containing many scenarios with various characteristics on the covariance structures of the explanatory variable, the types of outliers, the number of outliers, the location of active variables, and the number of variables.  The study then found that Tukey-LASSO outperformed Huber-LASSO and Welsch-LASSO in identifying significant variables.  The Robust LASSO performance generally decreased as the covariances among explanatory variables increased and the data dimension increased.  Exploration of sembung leaf extract data shows that the data is high dimensional data which contains outliers of about 14,28% on the response variable and about 25,71% on the explanatory variables.  Based on the research, the number of variables selected using the Tukey-LASSO method was nine compounds, Huber-LASSO and Welsch-LASSO were eight compounds, and LASSO 13 compounds.  The Tukey-LASSO prediction accuracy is superior to the other three methods.