International Conference on Computational Statistics (Compstat) edition:21 location:Genève, Switzerland date:19-22 August 2014
Multivariate multilevel data consist of multiple data blocks that all involve the same set of variables. For instance, one may think of personality measures of inhabitants from different countries. The associated research questions often pertain to the underlying covariance structure (e.g., which dimensions underlie the individual scores), and whether this structure holds for each data block (e.g., do inhabitants of different countries vary on the same personality dimensions). To answer such research questions, we present mixture simultaneous factor analysis (MSFA) which performs a clustering of the data blocks according to their covariance structure. MSFA, which is the stochastic counterpart of clusterwise simultaneous component analysis, is a multilevel latent variable model with continuous latent variables at the observation level (common factor models) and a discrete latent variable at the block level (according to mixture model). In other words, we assume that the data blocks are sampled from a mixture of multivariate normal distributions with different covariance matrices (note that existing multilevel mixture models assumed the covariances to be identical). MSFA can be applied by means of Latent GOLD.