An innovative strategy on the construction of multivariate multimodal linear mixed-effects models

This paper presents an attractive extension of multivariate mixed-effects models to allow the modeling of correlated responses. By initiating a new multivariate multimodal distribution, the proposed strategy takes multimodality and the asymmetric structure into account in a flexible way. It can also accommodate clustered random effects on multiple longitudinal responses when data comprise various hidden sub-populations that are not directly identifiable. We introduce an explicit stochastic hierarchical representation of the proposed model to render its theoretical properties straightforward and to carry out estimation processes easily. A fully Bayesian approach is proposed to compute posterior distributions using MCMC techniques in modeling multivariate longitudinal data. Moreover, we present an EM-based maximum likelihood estimation procedure. To facilitate Bayesian computation, the estimation process of mixed models utilizes a data augmentation scheme. We analyze two real-life data on the low-back pain study and the height of school-girls to illustrate the usefulness of our proposed model in practical applications.