Maximum Likelihood Analysis of a Two-Level Nonlinear Structural Equation Model With Fixed Covariates

Abstract

In this article, a maximum likelihood (ML) approach for analyzing a rather general two-level structural equation model is developed for hierarchically structured data that are very common in educational and/or behavioral research. The proposed two-level model can accommodate nonlinear causal relations among latent variables as well as effects of fixed covariate in its various components. Methods for computing the ML estimates, and the Bayesian information criterion (BIC) for model comparison are established on the basis of powerful tools in statistical computing such as the Monte Carlo EM algorithm, Gibbs sampler, Metropolis–Hastings algorithm, conditional maximization, bridge sampling, and path sampling. The newly developed procedures are illustrated by results obtained from a simulation study and analysis of a real data set in education.