A Nonlinear Dynamic Latent Class Structural Equation Model

In this article, we propose a nonlinear dynamic latent class structural equation modeling (NDLC-SEM). It can be used to examine intra-individual processes of observed or latent variables. These processes are decomposed into parts which include individual- and time-specific components. Unobserved heterogeneity of the intra-individual processes are modeled via a latent Markov process that can be predicted by individual- and time-specific variables as random effects. We discuss examples of sub-models which are special cases of the more general NDLC-SEM framework. Furthermore, we provide empirical examples and illustrate how to estimate this model in a Bayesian framework. Finally, we discuss essential properties of the proposed framework, give recommendations for applications, and highlight some general problems in the estimation of parameters in comprehensive frameworks for intensive longitudinal data.