A Bayesian approach for generalized random coefficient structural equation models for longitudinal data with adjacent time effects

This paper proposes a generalized random coefficient structural equation model for analyzing longitudinal data by incorporating the correlated structure due to adjacent time effects and by allowing structural parameters to vary across individuals. The coregionalization for modeling multivariate spatial data is adopted to formulate the correlated structure between adjacent time points. A Bayesian approach coupled with the Gibbs sampler and the Metropolis-Hastings algorithm is developed to obtain the Bayesian estimates of unknown parameters and latent variables simultaneously. A simulation study and a real example related to an emotion study are presented to illustrate the newly developed methodology.