There is increasing interest in modeling high-dimensional longitudinal outcomes in applications such as developmental neuroimaging research. Growth curve model offers a useful tool to capture both the mean growth pattern across individuals, as well as the dynamic changes of outcomes over time within each individual. However, when the number of outcomes is large, it becomes challenging and often infeasible to tackle the large covariance matrix of the random effects involved in the model. In this article, we propose a high-dimensional response growth curve model, with three novel components: a low-rank factor model structure that substantially reduces the number of parameters in the large covariance matrix, a re-parameterization formulation coupled with a sparsity penalty that selects important fixed and random effect terms, and a computational trick that turns the inversion of a large matrix into the inversion of a stack of small matrices and thus considerably speeds up the computation. We develop an efficient expectation-maximization type estimation algorithm, and demonstrate the competitive performance of the proposed method through both simulations and a longitudinal study of brain structural connectivity in association with human immunodeficiency virus.

翻译：在发育神经影像学等应用中，对高维纵向结果进行建模的兴趣日益增加。增长曲线模型提供了一种有用的工具，既能捕捉个体间的平均增长模式，也能捕捉每个个体内结果随时间动态变化。然而，当结果数量较大时，处理模型中涉及的随机效应的大协方差矩阵变得具有挑战性且通常不可行。在本文中，我们提出了一种高维响应增长曲线模型，包含三个新颖组成部分：一种低秩因子模型结构，大幅减少了大型协方差矩阵中的参数数量；一种结合稀疏惩罚的重新参数化公式，可筛选重要的固定和随机效应项；以及一种将大矩阵求逆转化为一组小矩阵求逆的计算技巧，从而显著加速计算。我们开发了一种高效的期望最大化类型估计算法，并通过模拟研究和一项关于脑结构连接性与人类免疫缺陷病毒关联的纵向研究，展示了该方法的竞争性能。