A robust lasso regression for linear mixed-effects models with diagnostic analysis

Abstract

Variable selection has been a topic of great interest for statisticians and researchers alike. The choice of the best subset of predictors may be carried out with the objective of improving prediction or for easier interpretation of results. However, such methods are not always straightforward, mainly in the context of linear mixed-effects models. Variable selection for such models must be carried out for both fixed and random effects, the first being related to the global mean of data and the second to subject-level variance. There are two possible approaches when selecting variables for mixed-effects models: joint or two-stage procedures. In existing literature on the topic of variable selection for linear mixed-effects model, there is a method of joint selection via lasso for linear mixed-effects models under a normal distribution. Another topic of remarkable importance, is diagnostics and residual analysis. While residual analyses are carried out to assess issues with the fitted model and identification of atypical observations, diagnostic analyses are carried out assuming the model as correct and, assessing its conclusions robustness to small disturbances in the data and/or the model. There are many possible ways to deal with such observations. One is using robust models, which are said to be robust to disturbances in the data. That is, models that are better fit to data sets that possess observations considered to be as outliers and/or leverage. This work aims to use the robust method for variable selection in linear mixed-effects model and compare it with the normal method using diagnostic analysis.