Intensive longitudinal data (ILD) collected in mobile health (mHealth) studies contain rich information on multiple outcomes measured frequently over time that have the potential to capture short-term and long-term dynamics. Motivated by an mHealth study of smoking cessation in which participants self-report the intensity of many emotions multiple times per day, we describe a dynamic factor model that summarizes the ILD as a low-dimensional, interpretable latent process. This model consists of two submodels: (i) a measurement submodel--a factor model--that summarizes the multivariate longitudinal outcome as lower-dimensional latent variables and (ii) a structural submodel--an Ornstein-Uhlenbeck (OU) stochastic process--that captures the temporal dynamics of the multivariate latent process in continuous time. We derive a closed-form likelihood for the marginal distribution of the outcome and the computationally-simpler sparse precision matrix for the OU process. We propose a block coordinate descent algorithm for estimation. Finally, we apply our method to the mHealth data to summarize the dynamics of 18 different emotions as two latent processes. These latent processes are interpreted by behavioral scientists as the psychological constructs of positive and negative affect and are key in understanding vulnerability to lapsing back to tobacco use among smokers attempting to quit.

翻译：移动健康（mHealth）研究收集的密集纵向数据（ILD）包含随时间频繁测量的多项结果，具有捕捉短期与长期动态的丰富信息。以一项关于戒烟的移动健康研究为背景——该研究中参与者每日多次报告多种情绪强度——我们提出一种动态因子模型，将密集纵向数据总结为低维可解释的潜在过程。该模型包含两个子模型：（i）测量子模型（因子模型），将多变量纵向结果总结为低维潜在变量；（ii）结构子模型（Ornstein-Uhlenbeck随机过程），在连续时间框架下捕捉多变量潜在过程的时序动态。我们推导了结果边际分布的封闭形式似然函数，以及OU过程计算更简便的稀疏精度矩阵。我们提出一种分块坐标下降算法用于参数估计。最后，将该方法应用于移动健康数据，将18种情绪的动态总结为两个潜在过程。行为科学家将这些潜在过程解释为积极情感与消极情感的心理构念，这对理解戒烟尝试者中复吸易感性的关键作用至关重要。