The Estimation Process in Bayesian Structural Equation Modeling Approach

Structural equation modelling (SEM) is a multivariate method that incorporates ideas from regression, path-analysis and factor analysis. A Bayesian approach to SEM may enable models that reflect hypotheses based on complex theory. The development and application of Bayesian approaches to SEM has, however, been relatively slow but with modern technology and the Gibbs sampler, is now possible. The Gibbs sampler can be used to obtain samples of arbitrary size from the posterior distribution over the parameters of a structural equation model (SEM) given covariance data and a prior distribution over the parameters. Point estimates, standard deviations and interval estimates for the parameters can be computed from these samples. This study shows that the conditional distributions required in the Gibbs sampler are familiar distributions, hence the algorithm is very efficient. A goodness of fit statistic for assessing the proposed model is presented. An illustrative example with a real data is presented.