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 & Bryk, 2002 Raudenbush, S. W., & Bryk, A. S. (2002). Hierarchical linear models: Applications and data analysis methods. Thousand Oaks, CA: Sage. [Google Scholar]), although alternative approaches are available when analyzing nested data (Binder & Roberts, 2003 Binder, D. A., & Roberts, G. R. (2003). Design-based and model-based methods for estimating model parameters. In R. L. Chambers & C. J. Skinner (Eds.), Analysis of survey data (pp. 29–48). Chichester, UK: Wiley & Sons.[Crossref] , [Google Scholar]; 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/10.1080/00273170903333574[Taylor & Francis Online], [Web of Science ®] , [Google Scholar]). The overarching goal of this article is to suggest when it is appropriate and advantageous to analyze such nested data within a single-level framework and when utilization of multilevel models presents advantages. The decision hinges on the research questions to be addressed, the scope of the data, and the measurement structure of any constructs hypothesized at the cluster level (Kozolowski & Klein, 2000 Kozolowski, S. W. J., & Klein, K. J. (2000). A multi-level approach to theory and research in organizations: Contextual, temporal, and emergent processes. In K. J. Klein & S. W. J. Kozlowski (Eds.), Multi-level theory, research, and methods in organizations: Foundations extensions, and new directions (pp, 3–90). San Francisco, CA: Jossey-Bass. [Google Scholar]; 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.