Statistical analysis of nonlinear structural equation models with continuous and polytomous data

A general nonlinear structural equation model with mixed continuous and pol ytomous variables is analysed. A Bayesian approach is proposed to estimate simultaneously the thresholds, the structural parameters and the latent var iables. To solve the computational difficulties involved in the posterior a nalysis, a hybrid Markov chain Monte Carlo method that combines the Gibbs s ampler and the Metropolis-Hasting algorithm is implemented to produce the B ayesian solution. Statistical inferences, which involve estimation of param eters and their standard errors, residuals and outliers analyses, and goodn ess-of-fit statistics for testing the posited model, are discussed. The pro posed procedure is illustrated by a simulation study and a real example.