The Differential Time-Varying Effect Model (DTVEM) of Jacobson et al. (2019) is a popular tool for finding the best time lag in intensive longitudinal data, but it assumes everyone shares the same lag structure. The original authors named fixing this as future work, and it clashes with the premise of modern clinical research, which is that people differ. We present DTVEM-RE, an extension that lets each person have their own lag coefficients, with two versions of the confirmatory step: a discrete-time hierarchical Bayesian VAR in Stan, which pools across people and gives calibrated uncertainty, and a continuous-time per-person Ornstein-Uhlenbeck model in ctsem, which handles unevenly spaced beeps directly. We report four results. A simulation shows the Bayesian version recovers the between-person spread tau_a with bias below 0.01 and coverage of 90 to 93 percent. On the Fisher et al. (2017) EMA dataset (N=40), person-specific lag-1 effects vary by an order of magnitude across three mood items, the Bayesian and GAMM estimates agree closely (r=0.87 to 0.92), and DTVEM-RE gives the best one-step-ahead prediction among four discrete-time methods. A multi-lag version shows all nine tau_k values have credible intervals excluding zero, and the lag where people differ most changes across items, something lag-1-only methods like mlVAR cannot detect. Finally, the two versions agree almost exactly on person-specific lag-1 estimates (r >= 0.995), differing only as shrinkage predicts. DTVEM-RE is, to our knowledge, the first person-specific implementation of DTVEM-style lag detection, and it contains standard DTVEM as a special case.

翻译：Jacobson等人（2019）提出的微分时变效应模型（DTVEM）是分析密集纵向数据中最佳时间滞后的常用工具，但其假设所有个体共享相同的滞后结构。原作者将该局限的修正列为未来工作方向，而这与现代临床研究“个体间存在差异”的基本前提相悖。我们提出DTVEM-RE扩展模型，允许每个个体拥有独立的滞后系数，并包含两种验证步骤实现方案：一是基于Stan实现的离散时间分层贝叶斯向量自回归模型，通过跨个体信息整合提供校准的不确定性估计；二是基于ctsem实现的连续时间个体特异性Ornstein-Uhlenbeck模型，可直接处理非等间隔测量数据。我们报告四项研究成果：模拟实验表明贝叶斯版本对个体间变异参数tau_a的估计偏差低于0.01，置信区间覆盖率为90%-93%；在Fisher等人（2017）的生态瞬时评估数据集（N=40）上，三种情绪维度的个体特异性滞后1期效应量存在数量级差异，贝叶斯方法与广义加性混合模型估计结果高度一致（r=0.87-0.92），且DTVEM-RE在四种离散时间方法中实现最优的一步向前预测；多滞后版本显示所有九项tau_k值的可信区间均不包含零，不同项目间个体差异最大的滞后位置存在变化，这是mlVAR等仅考虑滞后1期的方法无法检测的特征；两种实现方案在个体特异性滞后1期估计上近乎完全一致（r ≥ 0.95），仅存在符合收缩预期的细微差异。据我们所知，DTVEM-RE是首个实现DTVEM式滞后检测的个体特异性方法，且标准DTVEM模型可归为其特例。