On Bayesian estimation and model comparison of an integrated structural equation model

In this paper, we introduce a Bayesian approach to the estimation and model comparison of an integrated two-level nonlinear structural equation model with mixed continuous, dichotomous, and ordered categorical data that may be missing at random. This general model can accommodate nonlinearities of latent variables and the effects of fixed covariates on measurement and structural equations in within-groups and between-groups models. A sampling-based algorithm that combines the Gibbs sampler and the Metropolis–Hastings algorithm is proposed for posterior simulation. A procedure that utilizes path sampling is implemented to compute the Bayes factor for model comparison under the framework of the proposed integrated model. Empirical performances of Bayesian methodologies are illustrated via analysis of a real example.