Publications & Resources
Dealing with Measurement Error in Estimating a Cross-level Interaction: Nonlinear Multilevel Latent Variable Modeling Approach with a Metropolis-Hastings Robbins-Monro Algorithm
Ji Seung Yang and Li Cai
The main purpose of this study is to improve estimation efficiency in obtaining full information maximum likelihood (FIML) estimates of cross-level interactions in the framework of a nonlinear multilevel latent variable model by adopting the MetropolisHastngs
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 for a cross-level interaction model that requires high 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 cross-level interaction effect than the traditional approach. As an empirical illustration, a subset of data extracted from The Programme for International Student Assessment (PISA, 2000; OECD, 2000) was analyzed.
Yang, J. S., & Cai, L. (2014). Dealing with measurement error in estimating a cross-level interaction: Nonlinear multilevel latent variable modeling approach with a Metropolis-Hastings Robbins-Monro algorithm. KAERA Research Forum, 1(1), 55-71.