Estimation of Contextual Effects through Nonlinear Multilevel Latent Variable Modeling with a Metropolis-Hastings Robbins-Monro Algorithm

The main purpose of this study is to improve estimation efficiency in obtaining fullinformation maximum likelihood (FIML) estimates of contextual effects in the framework of nonlinear multilevel latent variable model by adopting the Metropolis-Hastings Robbins-Monro algorithm (MH-RM; Cai, 2008, 2010a, 2010b). Results indicate that the MH-RM algorithm can produce FIML estimates and their standard errors efficiently, and the efficiency of MH-RM was more prominent for a cross-level interaction model, which requires five dimensional integration. Simulations, with various sampling and measurement structure conditions, were conducted to obtain information about the performance of nonlinear multilevel latent variable modeling compared to traditional hierarchical linear modeling. Results suggest that nonlinear multilevel latent variable modeling can more properly estimate and detect a contextual effect and a cross-level interaction than the traditional approach. As empirical illustrations, two subsets of data extracted from Programme for International Student Assessment (PISA; OECD, 2000) were analyzed.