We consider the analysis of continuous repeated measurement outcomes that are collected longitudinally. A standard framework for analysing data of this kind is a linear Gaussian mixed effects model within which the outcome variable can be decomposed into fixed effects, time invariant and time‐varying random effects, and measurement noise. We develop methodology that, for the first time, allows any combination of these stochastic components to be non‐Gaussian, using multivariate normal variance–mean mixtures. To meet the computational challenges that are presented by large data sets, i.e. in the current context, data sets with many subjects and/or many repeated measurements per subject, we propose a novel implementation of maximum likelihood estimation using a computationally efficient subsampling‐based stochastic gradient algorithm. We obtain standard error estimates by inverting the observed Fisher information matrix and obtain the predictive distributions for the random effects in both filtering (conditioning on past and current data) and smoothing (conditioning on all data) contexts. To implement these procedures, we introduce an R package: ngme. We reanalyse two data sets, from cystic fibrosis and nephrology research, that were previously analysed by using Gaussian linear mixed effects models.

中文翻译：

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非高斯连续重复测量数据的线性混合效应模型

我们考虑对纵向收集的连续重复测量结果进行分析。用于分析此类数据的标准框架是线性高斯混合效应模型，在该模型中，结果变量可以分解为固定效应，时不变和时变随机效应以及测量噪声。我们开发了一种方法，这是第一次使用多元正态方差-均值混合将这些随机成分的任何组合设为非高斯分布。为了解决大型数据集所提出的计算难题，即在当前情况下，具有多个主题和/或每个主题许多重复测量的数据集，我们提出了一种新的实现方法，该方法使用基于计算的高效基于子采样的随机数进行最大似然估计梯度算法。我们通过反转观察到的Fisher信息矩阵获得标准误差估计，并获得滤波（对过去和当前数据的条件）和平滑（对所有数据的条件）上下文中的随机效应的预测分布。为了实现这些过程，我们引入了一个R包：ngme。我们重新分析了来自囊性纤维化和肾病学研究的两个数据集，这些数据先前已使用高斯线性混合效应模型进行了分析。