How best to model structurally heterogeneous processes is a foundational question in the social, health and behavioral sciences. Recently, Fisher et al., (2022) introduced the multi-VAR approach for simultaneously estimating multiple-subject multivariate time series characterized by common and individualizing features using penalized estimation. This approach differs from many popular modeling approaches for multiple-subject time series in that qualitative and quantitative differences in a large number of individual dynamics are well-accommodated. The current work extends the multi-VAR framework to include new adaptive weighting schemes that greatly improve estimation performance. In a small set of simulation studies we compare adaptive multi-VAR with these new penalty weights to common alternative estimators in terms of path recovery and bias. Furthermore, we provide toy examples and code demonstrating the utility of multi-VAR under different heterogeneity regimes using the multivar package for R (Fisher, 2022).

翻译：如何对结构异构过程进行最佳建模，是社会科学、健康科学和行为科学中的一个基础性问题。近期，Fisher等人（2022）引入了multi-VAR方法，通过惩罚估计同时估计具有共同特征与个体化特征的多主体多元时间序列。该方法与众多流行的多主体时间序列建模方法不同，能够很好地适应大量个体动态中的定性与定量差异。本研究扩展了multi-VAR框架，纳入新的自适应加权方案，显著提升了估计性能。通过一组小型模拟研究，我们从路径恢复和偏差两个角度，将自适应multi-VAR及其新惩罚权重与常见的替代估计器进行了比较。此外，我们还提供了示例和代码，利用R语言的multivar包（Fisher, 2022）展示了multi-VAR在不同异质性模式下的实用性。