Title: Robust Linear Mixed Models using Hierarchical Gamma-Divergence Show Chinese title

Title: 基于层次伽玛散度的鲁棒线性混合模型

Abstract: Linear mixed models (LMMs) are a popular class of methods for analyzing longitudinal and clustered data. However, such models can be sensitive to outliers, and this can lead to biased inference on model parameters and inaccurate prediction of random effects if the data are contaminated. We propose a new approach to robust estimation and inference for LMMs using a hierarchical gamma-divergence, which offers an automated, data-driven approach to downweight the effects of outliers occurring in both the error and the random effects, using normalized powered density weights. For estimation and inference, we develop a computationally scalable minorization-maximization algorithm for the resulting objective function, along with a clustered bootstrap method for uncertainty quantification and a Hyvarinen score criterion for selecting a tuning parameter controlling the degree of robustness. Under suitable regularity conditions, we show the resulting robust estimates can be asymptotically controlled even under a heavy level of (covariate-dependent) contamination. Simulation studies demonstrate hierarchical gamma-divergence consistently outperforms several currently available methods for robustifying LMMs. We also illustrate the proposed method using data from a multi-center AIDS cohort study. Show Chinese abstract

Abstract: 线性混合模型（LMMs）是一类用于分析纵向数据和聚类数据的流行方法。然而，这些模型可能对异常值敏感，如果数据受到污染，则可能导致模型参数的推断偏差以及随机效应预测的不准确性。我们提出了一种新的基于层次伽玛散度的鲁棒估计和推理方法，该方法通过使用标准化的幂密度权重，提供了自动化且数据驱动的方法来降低误差和随机效应中异常值的影响。为了估计和推理，我们开发了一个计算上可扩展的最小化-最大化算法来处理目标函数，并结合了聚类自助法来进行不确定性量化，以及一种Hyvarinen评分标准来选择控制鲁棒性的程度的调整参数。在适当的正则条件假设下，我们证明即使在重度（协变量依赖型）污染条件下，所得到的鲁棒估计也可以渐近控制。模拟研究显示层次伽玛散度在稳健化LMMs方面始终优于几种当前可用的方法。我们还利用多中心艾滋病队列研究的数据展示了所提出的方法。