Three-Step State Space Mixture Modeling to Compare Dynamic Processes Across Many Individuals

Researchers are often interested in modeling unobserved heterogeneity in dynamic processes of latent variables between individuals. This can be achieved with state space mixture modeling, a method that identifies discrete subgroups of individuals who follow qualitatively distinct processes. However, jointly estimating the measurement model of the latent variables, the structural model (the dynamic process), and the mixture components can be computationally demanding and fit indices conflate measurement model fit and structural model fit. Separating the estimation of measurement model and structural model offers faster computation time, easier interpretation of fit indices and various other advantages. To leverage these advantages, we present Three-Step State Space Mixture Modeling, an extension of the Three-Step Latent Vector Autoregression framework to state space mixture modeling. We demonstrate the method’s performance in obtaining correct estimates of the structural parameters and cluster memberships by means of a simulation study and illustrate the method with an empirical example.