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Abstract:
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The random effects selection has been received little attention in the literature. In linear mixed models, several methods for random effects selection have been proposed. However due to computationally intensive tasks, it is limited to apply the existing methods in practice. In this paper, we propose two approximate methods of the moment-based method for random effects selection. The exact moment-based method has two challenging computation issues: nonlinear semidefinite programming and nonlinear programming with a linear inequality constraint. In particular, the most time-consuming step is the second computation to produce sparse solutions of the variance-covariance matrix of random effect factors. Since the objective function has up to fourth order terms and it makes the computation tedious, we suggest using a linear approximation to the penalized variance-covariance matrix. It reduces the objective function up to second order, and the quadratic programming can be easily implemented in some statistical software. By simulation studies, we show that the approximate methods also perform well and often outperform the exact method.
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