Maximum likelihood estimation and model comparison of nonlinear structural equation models with continuous and polytomous variables

Recently, it is recognized that nonlinear relationships among latent variables in a structural equation model are important. In this article, maximum likelihood (ML) analysis of a general nonlinear structural equation model that contains fixed covariates in the measurement equation and the nonlinear structural equation is investigated. A MCEM algorithm is implemented to obtain the ML estimates, in which the E-step is completed with the help of a hybrid algorithm that combines the Gibbs sampler and the Metropolis-Hastings algorithm whilst the M-step is completed by conditional maximization. The importance sampling is employed to compute the observed-data likelihood in the Bayesian Information Criterion for model comparison. The methodology is illustrated with a simulation study and a real example. (C) 2002 Elsevier B.V. All rights reserved.