Latent Vector Autoregressive Modeling: A Stepwise Estimation Approach

Researchers often study dynamic processes of latent variables in everyday life, such as the interplay of positive and negative affect over time. An intuitive approach is to first estimate the measurement model of the latent variables, then compute factor scores, and finally use these factor scores as observed scores in vector autoregressive modeling. However, this approach neglects the uncertainty in the factor scores, leading to biased parameter estimates and threatening the validity of conclusions about the dynamic process. We propose Three-Step Latent Vector Autoregression that adheres to this stepwise procedure while correcting for the factor scores’ uncertainty. Stepwise approaches offer various advantages, for example the ability to visualize and inspect the factor scores. A simulation study demonstrates that the method performs well in obtaining correct parameter estimates of a dynamic process. We also provide an empirical example and scripts for implementation in the open-source software R using the <i>lavaan</i> package.

研究者常于日常生活场景中探究潜变量（latent variables）的动态过程，例如正负情绪随时间推移的交互作用。一种直观的研究路径为先估计潜变量的测量模型，再计算因子得分（factor scores），最终将这些因子得分作为观测得分纳入向量自回归建模（vector autoregressive modeling）。然而该方法忽略了因子得分的不确定性，会导致参数估计有偏，进而威胁动态过程相关结论的效度。本研究提出三步潜变量向量自回归（Three-Step Latent Vector Autoregression）方法，该方法遵循上述分步流程的同时，校正了因子得分的不确定性。分步建模方法具备多项优势，例如可对因子得分进行可视化与检视。模拟研究表明，本方法在获取动态过程的准确参数估计方面表现优异。本研究还提供了一则实证案例，以及基于开源软件R、使用lavaan包实现的代码脚本。