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<p>The assumption of normality in random effects and regression errors is the primary cause of the lack of robustness in the maximum likelihood estimation procedure for linear mixed models. In this paper, we introduce a robust method for estimating regression parameters in these models, by positing that the random effects and regression errors follow a multivariate Laplace distribution. This new methodology, implemented via an EM algorithm, is computationally more efficient compared to the existing robust <i>t</i> procedure in the literature. Simulation studies suggest that the performance of the proposed estimation method in finite samples either surpasses or is at least on par with the robust <i>t</i> procedure.</p>

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Robust mixture of linear mixed modeling via multivariate Laplace distribution

  • 期刊论文

  • 发表日期：

    2025年3月24日

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  • Xiongya Li,
  • Xiuqin Bai,
  • Weixing Song

摘要

The assumption of normality in random effects and regression errors is the primary cause of the lack of robustness in the maximum likelihood estimation procedure for linear mixed models. In this paper, we introduce a robust method for estimating regression parameters in these models, by positing that the random effects and regression errors follow a multivariate Laplace distribution. This new methodology, implemented via an EM algorithm, is computationally more efficient compared to the existing robust t procedure in the literature. Simulation studies suggest that the performance of the proposed estimation method in finite samples either surpasses or is at least on par with the robust t procedure.