Bayesian Analysis of Structural Equation Model With Fixed Covariates

Abstract

This article extends the LISREL model to incorporate fixed covariates at both the measurement and the structural equations of the model. A Bayesian procedure with conjugate type prior distributions is established. The joint Bayesian estimates of the latent variables and the structural parameters that involve the regression coefficients of the covariates, the variances, covariances and causations among the manifest and latent variables are obtained via the Gibbs sampler algorithm. It is shown 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 some real data is presented.