A combined multilevel factor analysis and covariance regression model with mixed effects in the mean and variance structure.

Li et al developed a multilevel covariance regression (MCR) model as an extension of the covariance regression model of Hoff and Niu. This model assumes a hierarchical structure for the mean and the covariance matrix. Here, we propose the combined multilevel factor analysis and covariance regression model in a Bayesian framework, simultaneously modeling the MCR model and a multilevel factor analysis (MFA) model. The proposed model replaces the responses in the MCR part with the factor scores coming from an MFA model. Via a simulation study and the analysis of real data, we show that the proposed model is quite efficient when the responses of the MCR model are not measured directly but are latent variables such as the patient experience measurements in our motivating dataset.