Multilevel Mixture Factor Models

Factor analysis is a statistical method for describing the associations among sets of observed variables in terms of a small number of underlying continuous latent variables. Various authors have proposed multilevel extensions of the factor model for the analysis of data sets with a hierarchical structure. These Multilevel Factor Models (MFMs) have in common that-as in multilevel regression analysis-variation at the higher level is modeled using continuous random effects. In this article, we present an alternative multilevel extension of factor analysis which we call the Multilevel Mixture Factor Model (MMFM). It is based on the assumption that higher level units belong to latent classes that differ in terms of the parameters of the factor model specified for the lower level units. We demonstrate the added value of MMFM compared with MFM, both from a theoretical and applied perspective, and we illustrate the complementarity of the two approaches with an empirical application on students' satisfaction with the University of Florence. The multilevel aspect of this application is that students are nested within study programs, which makes it possible to cluster these programs based on their differences in students' satisfaction.