Latent Vector Autoregressive Modeling: A Stepwise Estimation Approach

Abstract

Researchers often study dynamic processes of latent variables in everyday life, such as the interplay of positive and negative affect across consecutive time-points. An intuitive approach is to first estimate the measurement model of the latent variables, then compute factor scores, and finally use these scores as observed scores in vector autoregressive modeling. However, this approach neglects the uncertainty in the factor scores, which biases the parameter estimates and threatens 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. Through a simulation study, we demonstrate that the method performs well in obtaining correct parameter estimates of a bivariate dynamic process. We further illustrate the application of the method with an empirical example and provide researchers with scripts to implement the method in the open-source software R using the lavaan package.