In longitudinal studies, repeated measures are collected over time and hence they tend to be serially correlated. These studies are commonly analyzed using linear mixed models (LMMs), and in this article we consider an extension of the skew‐normal/independent LMM, where the error term has a dependence structure, such as damped exponential correlation or autoregressive correlation of order p. The proposed model provides flexibility in capturing the effects of skewness and heavy tails simultaneously when continuous repeated measures are serially correlated. For this robust model, we present an efficient EM‐type algorithm for parameters estimation via maximum likelihood and the observed information matrix is derived analytically to account for standard errors. The methodology is illustrated through an application to schizophrenia data and some simulation studies. The proposed algorithm and methods are implemented in the new R package skewlmm.

中文翻译：

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具有对象内序列依赖性的偏正态线性混合模型的比例混合

在纵向研究中，随着时间的推移会收集重复的度量，因此它们往往是连续相关的。这些研究通常使用线性混合模型（LMM）进行分析，在本文中，我们考虑偏正态/独立LMM的扩展，其中误差项具有依赖性结构，例如p阶阻尼指数相关或自回归相关。当连续重复测量连续相关时，所提出的模型提供了灵活性，可以同时捕获偏斜和重尾巴的影响。对于这个健壮的模型，我们提出了一种有效的EM类型算法，用于通过最大似然估计参数，并通过分析得出观察到的信息矩阵以解决标准误差。通过对精神分裂症数据的应用和一些模拟研究说明了该方法。所提出的算法和方法在新的R包框架中实现。