Mixed effect models are fundamental tools for 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. In this paper, we propose a simple iterative procedure that estimates and selects fixed and random effects for linear mixed models. In particular, we propose to utilize the partial consistency property of the random effect coefficients and select groups of random effects simultaneously via a data-oriented penalty function (the smoothly clipped absolute deviation penalty function). We show that the proposed method is a consistent variable selection procedure and possesses some oracle properties. Simulation studies and a real data analysis are also conducted to empirically examine the performance of this procedure.
