ABSTRACT The linear mixed model with an added integrated Ornstein–Uhlenbeck (IOU) process (linear mixed IOU model) allows for serial correlation and estimation of the degree of derivative tracking. It is rarely used, partly due to the lack of available software. We implemented the linear mixed IOU model in Stata and using simulations we assessed the feasibility of fitting the model by restricted maximum likelihood when applied to balanced and unbalanced data. We compared different (1) optimization algorithms, (2) parameterizations of the IOU process, (3) data structures and (4) random-effects structures. Fitting the model was practical and feasible when applied to large and moderately sized balanced datasets (20,000 and 500 observations), and large unbalanced datasets with (non-informative) dropout and intermittent missingness. Analysis of a real dataset showed that the linear mixed IOU model was a better fit to the data than the standard linear mixed model (i.e. independent within-subject errors with constant variance).

中文翻译：

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线性混合积分 Ornstein-Uhlenbeck 模型的估计

摘要 线性混合模型与添加的集成 Ornstein-Uhlenbeck (IOU) 过程（线性混合 IOU 模型）允许序列相关和导数跟踪程度的估计。它很少使用，部分原因是缺乏可用的软件。我们在 Stata 中实现了线性混合 IOU 模型，并使用模拟评估了在应用于平衡和不平衡数据时通过限制最大似然拟合模型的可行性。我们比较了不同的 (1) 优化算法，(2) IOU 过程的参数化，(3) 数据结构和 (4) 随机效应结构。当应用于大型和中等规模的平衡数据集（20,000 和 500 个观测值）以及具有（非信息性）丢失和间歇性缺失的大型不平衡数据集时，拟合模型是实用且可行的。