Robust variable selection in semiparametric mixed effects longitudinal data models

Abstract

In this paper, we present a robust joint variable selection procedure for fixed and random effects in semiparametric linear mixed effects model for longitudinal data. Our simultaneous selection method overcomes the defects of typical approaches which select separately each of the two effects components. Meanwhile, the proposed procedure performs better than nonrobust method when there are outliers in the data. This method is based on a robustified penalized joint likelihood of the reparameterized linear mixed effects model through B-splines approximation and Cholesky decomposition. It is further shown that the robust variable selection method enjoys the Oracle property. We demonstrate the performance of the method based on a simulation study in the end.