Multilevel and Single-Level Models for Measured and Latent Variables When Data Are Clustered

Multilevel models are often used to evaluate hypotheses about relations among constructs when data are nested within clusters (Raudenbush Sterba, 2009 Sterba, S. K. (2009). Alternative model-based and design-based frameworks for inference from samples to populations: From polarization to integration. Multivariate Behavioral Research, 44, 711–740. http://dx.doi.org/10.1080/00273170903333574Taylor Marsh et al., 2012 Marsh, H. W., Ludtke, O., Nagengast, B., Trautwein, U., Morin, A. J. S., Abduljabbar, A. S., & Koller, O. (2012). Classroom climate and contextual effects: Conceptual and methodological issues in the evaluation of group-level effects. Educational Psychologist, 47, 106–124. http://dx.doi.org/10.1080/00461520.2012.670488[Taylor & Francis Online, Web of Science ® , Google Scholar). We demonstrate models using several different data sets, including single-level and multilevel hierarchical linear models and confirmatory factor models. For these demonstrations, observational data from students nested within schools are used, as well as data from a classroom-based cluster randomized trial.