Title: Mixture simultaneous factor analysis and Wald tests for factor loading differences in multivariate multilevel data
Authors: Kim De Roover - KU Leuven (Belgium) [presenting]
Jeroen Vermunt - Tilburg University (Netherlands)
Marieke Timmerman - University of Groningen (Netherlands)
Eva Ceulemans - University of Leuven (Belgium)
Abstract: Multivariate multilevel data consist of multiple data blocks involving the same variables; for instance, inhabitants from different countries rating emotion norms. The associated research questions often pertain to the underlying covariance structure (e.g. which dimensions underlie the individual scores), and whether it holds for each data block (e.g. do the underlying dimensions differ across countries). To answer such questions, mixture simultaneous factor analysis (MSFA) performs a mixture clustering of the blocks according to their factor structure, ignoring mean differences. Specifically, MSFA assumes that the data are sampled from a mixture of multivariate normal distributions with different covariance matrices, modeled by a low rank factor model, and that all individuals within a block are sampled from the same distribution. Comparing the cluster-specific factor loadings, one may either detect that the data blocks differ completely in underlying dimensions, or that only a few variables behave differently in some blocks. By simulations and empirical analysis using Latent Gold, we evaluate how well Wald-tests for loading differences can determine which variables make out the between-block structural differences.