典型基本偏t线性混合模型
Canonical fundamental skew-t linear mixed models
摘要：
在临床试验中，研究经常呈现纵向数据或聚类数据。这些研究通常使用线性混合模型（LLM）进行分析，通常考虑随机效应和误差项的高斯假设。最近，一些提案扩展了传统LMM的限制性假设，通过更灵活的假设，可以适应偏度和重尾，因此对离群值更鲁棒。本文提出了一个典型的基本偏t线性混合模型（ST-LMM），它允许非对称和重尾随机效应和误差，并包括几个重要的情况作为特殊情况，这是提出和考虑模型选择。对于这个强大的和灵活的模型，我们提出了一个有效的EM型算法参数估计通过极大似然，实现在一个封闭的形式，通过探索的ST-LMM的分层表示。此外，还讨论了标准误和随机效应的估计。该方法是通过应用程序来说明精神分裂症的数据和一些模拟研究。
英文摘要：
In clinical trials, studies often present longitudinal data or clustered data. These studies are commonly analyzed using linear mixed models (LMMs), usually considering Gaussian assumptions for random effect and error terms. Recently, several proposals extended the restrictive assumptions from traditional LMM by more flexible ones that can accommodate skewness and heavy-tails and consequently are more robust to outliers. This work proposes a canonical fundamental skew-t linear mixed model (ST-LMM), that allows for asymmetric and heavy-tailed random effects and errors and includes several important cases as special cases, which are presented and considered for model selection. For this robust and flexible model, we present an efficient EM-type algorithm for parameter estimation via maximum likelihood, implemented in a closed form by exploring the hierarchical representation of the ST-LMM. In addition, the estimation of standard errors and random effects is discussed. The methodology is illustrated through an application to schizophrenia data and some simulation studies.
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