Variable Selection with Shrinkage Methods in Elliptical Linear Mixed Models

Linear Mixed Models (LMM) provide a common and convenient framework for the analysis of longitudinal and clustered data by incorporating random effects. The main assumption of classical LMM is having normally distributed random effects and error terms. However, there are several situations in which we need to use more robust distributions rather than (multivariate) normal to handle heavy tailed data or outliers. In this study, we aim to do variable selection in LMM with elliptically distributed random effects and error terms with the goal of more robust parameter estimation and variable selection. Recently, shrinkage methods emerged as efficient variable selection methods and one of the shrinkage methods is adapted into elliptical LMM. Both simulation studies and a real data example show that, if the variable selection is also a concern, it is worthwhile to carry on the variable selection and the parameter estimation simultaneously in elliptical LM