Students Reading Motivation: A Multilevel Mixture Factor Analysis

Latent variable modeling is a commonly used data analysis tool in social sciences and other applied fields. The most popular latent variable models are factor analysis (FA) and latent class analysis (LCA). FA assumes that there is one or more continuous latent variables – called factors – determining the responses on a set of observed variables, while LCA assumes that there is an underlying categorical latent variable – latent classes. Mixture FA is a recently proposed combination of these two models which includes both continuous and categorical latent variables. It simultaneously determines the dimensionality (factors) and the heterogeneity (latent classes) of the observed data. Both in social sciences and in biomedical field, researchers often encounter multilevel data structure. These are usually analyzed using models with random effects. Here, we present a hierarchical extension of FA called multilevel mixture factor analysis (MMFA) (Varriale and Vermunt, Multilevel mixture factor models, Under review). As in multilevel LCA (Vermunt, Sociol Methodol 33:213–239, 2003), the between-group heterogeneity is modeled by assuming that higher-level units belong to one of K latent classes. The key difference with the standard mixture FA is that the discrete mixing distribution is at the group level rather than at the individual level. We present an application of MMFA in educational research. More specifically, a FA structure is used to measure the various dimensions underlying pupils reading motivation. We assume that there are latent classes of teachers which differ in their ability of motivating children. D. Riggi ( ) Department of Statistics, University of Milan-Bicocca, Via Bicocca degli Arcimboldi 8, Ed. U7, Milan, Italy e-mail: [email protected] J.K. Vermunt Department of Methodology and Statistics, Tilburg University, P.O. Box 90153, 5000 LE, Tilburg, The Netherlands e-mail: [email protected] W. Gaul et al. (eds.), Challenges at the Interface of Data Analysis, Computer Science, and Optimization, Studies in Classification, Data Analysis, and Knowledge Organization, DOI 10.1007/978-3-642-24466-7 58, © Springer-Verlag Berlin Heidelberg 2012 567 568 D. Riggi and J.K. Vermunt