Simulation Study to Describe Bayesian Analysis of Nonlinear Structural Equation Modeling

Structural equation modeling (SEM) has widely used in many disciplines, such as economic, politic or health. Nonlinear structural equation modeling, as part of SEM, also has been developing analytically but still limited. In this method, the parameter models are estimated using conjugate prior in Bayesian approach. In nonlinear SEM, the models are specified including quadratic forms and/or interactions of latent variables. Posterior mean and posterior variance of the parameters are estimated using iteration approach since it is difficult to estimate those parameters model using analytical approach. The iteration approach used here is Markov Chain Monte Carlo (MCMC) method with Gibbs sampling. The simulation study is done to illustrate the proposed estimation methods for nonlinear model. A group of 300 data are generated to demonstrate the implementation of the proposed method. This study resulted that the proposed nonlinear SEM model could be accepted based on criteria of goodness of fit model.