统计研究

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高维混合效应模型的双正则化分位回归方法研究

罗幼喜等   

  • 出版日期:2017-07-15 发布日期:2017-07-18

The Research of Dual Regularized Quantile Regression for High Dimensional Mixed Effect Models

Luo Youxi et al.   

  • Online:2017-07-15 Published:2017-07-18

摘要: 针对高维混合效应模型,文章提出了一种双正则化分位回归方法。通过对随机和固定效应系数同时实施L1正则化惩罚,该方法一方面能够对重要解释变量进行挑选,另一方面也能够消除个体随机波动带来的偏差。求解参数估计的交替迭代算法不仅破解了要同时确定两个调整参数的难题,而且算法速度快。模拟结果也表明该方法不仅对误差类型有很强的抗干扰能力,同时在模型有不同稀疏程度时均表现良好,尤其是对于解释变量多于样本的高维情况。为了方便在实际问题中选择最优正则化参数,文章还对两种参数选取标准进行了比较研究。最后利用新方法对一个教育方面的数据给予了实证演示,找出了在各个分位点处对学生成绩有影响的重要因素。

关键词: 高维混合效应模型, 双正则化, 交替迭代法

Abstract: The paper proposes a dual regularized quantile regression method for high dimensional mixed effects model, that is, by applying the L1 penalty to the fixed and random effect coefficients, the method can select the important predictive variables in the mixed effect model meanwhile fully taking into account the impact of unknown random effects. The iterative algorithm designed for parameter estimation not only solves the dilemma of selecting two regularization parameters, but also converges quickly. Computer simulation studies show that the new method is not only robust to the random error distribution, but also has good performance even under different sparse models, especially for the high-dimensional case. In this paper, the characteristics of two regularization parameter selection criteria are compared by simulation results, so as to use them in practical problems. Finally, the proposed method is used to analyze an educational data, and the key factors that affect the students' score at different quantiles are given.

Key words: High Dimensional Mixed Effects Model, Dual Regularization, Alternating Iterative Method