Analysis of Generalized Nonlinear Structural Equation Models by Using Bayesian Approach with Application

Abstract

In this paper, Bayesian analysis is used in nonlinear structural equation models with two population of data and the Gibbs sampling method is applied for estimation and model comparison. Hidden continuous normal distribution (censored normal distribution) is used to solve the problem of ordered categorical data in Bayesian multiple group SEMs and compared with the method that treats ordered categorical variables as a continuous normal distribution. Statistical inferences, which involve the estimation of parameters and their standard errors, and residuals analyses for testing the posited model are discussed. The proposed procedure is illustrated using real data with the results obtained from the WinBUGS program.