Abbott Madeline R, Dempsey Walter H, Nahum-Shani Inbal, Lam Cho Y, Wetter David W, Taylor Jeremy M G
Department of Biostatistics, https://ror.org/00jmfr291University of Michigan, Ann Arbor, MI, USA.
Institute for Social Research, https://ror.org/00jmfr291University of Michigan, Ann Arbor, MI, USA.
Psychometrika. 2025 Jun 16:1-22. doi: 10.1017/psy.2025.10023.
Intensive longitudinal data (ILD) collected in mobile health (mHealth) studies contain rich information on the dynamics of multiple outcomes measured frequently over time. Motivated by an mHealth study in which participants self-report the intensity of many emotions multiple times per day, we describe a dynamic factor model that summarizes ILD as a low-dimensional, interpretable latent process. This model consists of (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 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 and use simulation studies to show that it has good statistical properties with ILD. Then, we use our method to analyze data from the mHealth study. We summarize the dynamics of 18 emotions using models with one, two, and three time-varying latent factors, which correspond to different behavioral science theories of emotions. We demonstrate how results can be interpreted to help improve behavioral science theories of momentary emotions, latent psychological states, and their dynamics.
移动健康（mHealth）研究中收集的密集纵向数据（ILD）包含了关于多个随时间频繁测量的结果动态变化的丰富信息。受一项mHealth研究的启发，在该研究中参与者每天多次自我报告多种情绪的强度，我们描述了一种动态因子模型，该模型将ILD总结为一个低维的、可解释的潜在过程。该模型由（i）一个测量子模型——一个因子模型——将多变量纵向结果总结为低维潜在变量，以及（ii）一个结构子模型——一个奥恩斯坦 - 乌伦贝克（OU）随机过程——在连续时间内捕捉多变量潜在过程的动态变化。我们推导了结果边际分布的闭式似然以及OU过程计算更简单的稀疏精度矩阵。我们提出了一种用于估计的块坐标下降算法，并通过模拟研究表明它对ILD具有良好的统计特性。然后，我们使用我们的方法分析来自mHealth研究的数据。我们使用具有一、二和三个随时间变化的潜在因子的模型总结了18种情绪的动态变化，这些模型对应于不同的情绪行为科学理论。我们展示了如何解释结果以帮助改进关于瞬间情绪、潜在心理状态及其动态变化的行为科学理论。
