Publications & Resources
Estimation of Contextual Effects Through Nonlinear Multilevel Latent Variable Modeling With a Metropolis-Hastings Robbins-Monro Algorithm
Ji Seung Yang and Li Cai
The main purpose of this study is to improve estimation ef?ciency in obtaining full-information maximum likelihood (FIML) estimates of contextual effects in the frame-work 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 ef?ciently, and the ef?ciency of MH-RM was more prominent for a cross-level interaction model, which requires ?ve dimensional integration. Simulations, with various sampling and measure-ment structure conditions, were conducted to obtain information about the performance of nonlinear multilevel latent variable modeling compared to traditional hierarchical lin-ear 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.
Yang, J. S., & Cai, L. (2013, April). Estimation of contextual effects through nonlinear multilevel latent variable modeling with a MetropolisHastings Robbins-Monro algorithm. Paper presented at the annual meeting of the American Educational Research Association, San Francisco, CA.