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 lavaan package.