Linear mixed effects models (LMEM) play an important role in the analysis of longitudinal 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. This talk is concerned with the selection and estimation of the fixed and random effects in LMEM. We propose a new variable selection method for LMEM, named broken adaptive ridge (BAR) regression which incorporates the merits of $L_{0}$ 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 $L_{0}$-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. Numerical studies are conducted to investigate and illustrate the efficacy of LMEM via BAR in comparison with other methods.