Title: A new approach to variable selection in linear mixed effect models via broken adaptive ridge regression
Authors: Hong Yin - Renmin University of China (China) [presenting]
Gang Li - University of California at Los Angeles (United States)
Abstract: Linear mixed effect models (LMEM) play an important role in the analysis of longitudinal data, panel data and cross-sectional data. They are widely used by various fields of social sciences, medical and biological sciences. However, the complex nature of these models has made variable selection and parameter estimation a challenging problem. The selection and estimation of the fixed and random effects in LMEM are considered. We propose a new variable selection method for LMEM, named broken adaptive ridge (BAR) regression which incorporates the merits of L0 penalized regression with those of ridge regression. Definitely, it is an iterative version of ridge regression in which each coefficient will be given a updated weighted score related to the last coefficients values. Due to inheriting some properties of L0-penalized regression in a sense that it can choose the non-zero components and shrink the zero components quickly, accurately and unhesitatingly. At the same time, it reserves the version of ridge regression, so there is no much burden in the optimization of objective function. We also show that the proposed method is consistent variable selection procedure and possesses some oracle properties. The results of simulation data sets and a real data have shown the efficacy of our method compared with the smoothly clipped absolute deviation penalty (SCAD).