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Non-concave penalization in linear mixed-effect models and regularized selection of fixed effects

机译：线性混合效应模型中的非凹形惩罚和固定效应的正规选择

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摘要

Mixed-effect models are very popular for analyzing data with a hierarchical structure. In medical applications, typical examples include repeated observations within subjects in a longitudinal design, patients nested within centers in a multicenter design. However, recently, due to the medical advances, the number of fixed-effect covariates collected from each patient can be quite large, e.g., data on gene expressions of each patient, and all of these variables are not necessarily important for the outcome. So, it is very important to choose the relevant covariates correctly for obtaining the optimal inference for the overall study. On the other hand, the relevant random effects will often be low-dimensional and pre-specified. In this paper, we consider regularized selection of important fixed-effect variables in linear mixed-effect models along with maximum penalized likelihood estimation of both fixed and random-effect parameters based on general non-concave penalties. Asymptotic and variable selection consistency with oracle properties are proved for low-dimensional cases as well as for high dimensionality of non-polynomial order of sample size (number of parameters is much larger than sample size). We also provide a suitable computationally efficient algorithm for implementation. Additionally, all the theoretical results are proved for a general non-convex optimization problem that applies to several important situations well beyond the mixed model setup (like finite mixture of regressions) illustrating the huge range of applicability of our proposal.
机译：混合效果模型非常流行用于分析具有层次结构的数据。在医疗应用中，典型示例包括在纵向设计中对受试者进行重复观察，在多中心设计中将患者嵌套在中心内。然而，近来，由于医学的进步，从每个患者收集的固定作用协变量的数量可能非常大，例如，关于每个患者的基因表达的数据，并且所有这些变量对于结果不一定都是重要的。因此，正确选择相关协变量对于获得整体研究的最佳推断非常重要。另一方面，相关的随机效应通常是低维的并且是预先指定的。本文考虑线性混合效应模型中重要固定效应变量的正规化选择，以及基于一般非凹面惩罚的固定效应和随机效应参数的最大惩罚似然估计。在低维情况下以及在高维数的非多项式样本量（参数数量比样本量大得多）的情况下，证明了具有oracle属性的渐近和变量选择一致性。我们还提供了合适的计算有效算法来实现。此外，所有的理论结果都被证明适用于一般的非凸优化问题，该问题不仅适用于混合模型设置（例如回归的有限混合），而且还适用于几种重要情况，说明了我们建议的广泛适用性。

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  • 来源
    《Advances in statistical analysis》 |2018年第2期|179-210|共32页
  • 作者

    Ghosh Abhik; Thoresen Magne;

  • 作者单位

    Univ Oslo, Dept Biostat, Oslo Ctr Biostat & Epidemiol, Oslo, Norway;

    Univ Oslo, Dept Biostat, Oslo Ctr Biostat & Epidemiol, Oslo, Norway;

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