Given multivariate data, many research questions pertain to the covariance structure: whether and how the variables (for example, personality measures) covary. Exploratory factor analysis (EFA) is often used to look for latent variables that may explain the covariances among variables; for example, the Big Five personality structure. In case of multilevel data, one may wonder whether or not the same covariance (factor) structure holds for each so-called ‘data block’ (containing data of one higher-level unit). For instance, is the Big Five personality structure found in each country or do cross-cultural differences exist? The well-known multigroup EFA framework falls short in answering such questions, especially for numerous groups/blocks. We introduce mixture simultaneous factor analysis (MSFA), performing a mixture model clustering of data blocks, based on their factor structure. A simulation study shows excellent results with respect to parameter recovery and an empirical example is included to illustrate the value of MSFA.
De Roover, K., Vermunt, J. K., Timmerman, M. E., & Ceulemans, E. (2017). Mixture simultaneous factor analysis for capturing differences in latent variables between higher level units of multilevel data. Structural Equation Modeling, 24(4), 506-523. https://doi.org/10.1080/10705511.2017.1278604