The methodology of multilevel factor analysis

• In Event: Multilevel Latent Variable Models: The Next Generation

Abstract

In this paper, we present an explication of the emerging analytic method called multi-level factor analysis (MLFA) that can be used to provide a novel approach for conceptualizing, measuring, and modeling environments, including school climate (Dedrick & Greenbaum, 2011; Dyer, Hanges, & Hall, 2005; Reise, Ventura, Neuchterlein, & Kim, 2005; Toland & De Ayala, 2005). MLFA is similar to all factor analytic methods in that it seeks to capture the shared variance among an observed set of variables in terms of a potentially smaller number of unobserved constructs or latent factors (Brown, 2006; Kline, 2010). Like all factor analyses, MLFA uses the observed variance-covariance matrix for a set of observed variables to estimate a set of measurement parameters, which describe the relationships between the observed variables and the underlying latent factor.

However, MLFA differs from a traditional factor analysis in one major way. Specifically, as the name implies, it is multi-level. Unlike a single-level exploratory or confirmatory factor analysis, which estimates latent factors at only one level (i.e. the individual or contextual level), MLFA decomposes the total sample variance-covariance matrix into within-group (i.e. individual-level, within a context) and between-group (i.e. contextual-level) matrices and simultaneously models distinct latent factor structures at each of these levels (Hox, 2010; Muthen, 1991, 1994). By modeling two different latent factor structures, researchers are better able to understand the variation that exists between individuals within an environment as well as between environments, rather than assuming the factor structure is the same at both levels.

Authors

• Katherine E. Masyn, Harvard University

• Erin Dunn, Harvard University