Multivariate outcomes with heavy skewness and thick tails often arise from clustered experiments or longitudinal studies. Linear mixed models with multivariate skew-t (MST) distributions for the random effects and the error terms is a popular tool of robust modeling for such outcomes. However the usual MST distribution only allows a common degree of freedom for all marginal distributions, which is only appropriate when each marginal has the same amount of tail heaviness. In this paper, we introduce a new class of extended MST distributions, which allow different degrees of freedom and thereby can accommodate heterogeneity in tail-heaviness across outcomes. The extended MST distributions yield a flexible family of models for multivariate outcomes. The hierarchical representation of the MST distribution allows MCMC methods to be easily applied to compute the parameter estimates. The proposed model is applied to data from two biomedical studies: one on bivariate markers of AIDS progression and the other on sexual behavior from a longitudinal study.

中文翻译：

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使用扩展多元 skew-$t$ 分布的多种结果的线性混合模型

具有严重偏度和粗尾的多变量结果通常来自集群实验或纵向研究。具有随机效应和误差项的多元偏斜 (MST) 分布的线性混合模型是对此类结果进行稳健建模的流行工具。然而，通常的 MST 分布只允许所有边际分布具有共同的自由度，这仅适用于每个边际具有相同数量的尾部重量。在本文中，我们引入了一类新的扩展 MST 分布，它允许不同的自由度，从而可以适应不同结果的尾重的异质性。扩展的 MST 分布为多变量结果生成了灵活的模型系列。MST 分布的分层表示允许轻松地应用 MCMC 方法来计算参数估计。所提出的模型应用于两项生物医学研究的数据：一项关于艾滋病进展的双变量标记，另一项关于来自纵向研究的性行为。