Semiparametric mixed-effects models (SMM) have received increasing attention in recent years because of the greater flexibility in analysing longitudinal trajectories. However, the normality assumption of SMM may be unrealistic when outliers occur in the data. This paper presents a semiparametric extension of the multivariate t linear mixed-effects model (MtLMM), called the multivariate t semiparametric mixed model (MtSMM). To be specific, the MtSMM incorporates a parametric linear function related to the fixed covariate effects and random effects which have a joint multivariate t distribution together with an arbitrary nonparametric smooth function to capture the unexpected patterns. A computationally analytical EM-based algorithm is developed for carrying out maximum likelihood estimation of the MtSMM. Simulation studies and a real example concerning the analysis of PBCseq data are used to investigate the empirical behaviour of the proposed methodology.

中文翻译：

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多特征纵向数据的多元t半参数混合效应模型

由于在分析纵向轨迹方面具有更大的灵活性，半参数混合效应模型 (SMM) 近年来受到越来越多的关注。然而，当数据中出现异常值时，SMM 的正态性假设可能不切实际。本文介绍了多元 t 线性混合效应模型 (MtLMM) 的半参数扩展，称为多元 t 半参数混合模型 (MtSMM)。具体来说，MtSMM 结合了与固定协变量效应和随机效应相关的参数线性函数，它们具有联合多元 t 分布以及任意非参数平滑函数来捕获意外模式。开发了一种基于计算分析的 EM 算法，用于执行 MtSMM 的最大似然估计。