Grouped multi-trajectory modeling using finite mixtures of multivariate contaminated normal linear mixed model

There has been growing interest across various research domains in the modeling and clustering of multivariate longitudinal trajectories obtained from internally near-homogeneous subgroups. One prominent motivation for such work arises from the Alzheimer's Disease Neuroimaging Initiative (ADNI) cohort study, which involves multiple clinical measurements, exhibiting complex features such as diverse progression patterns, multimodality, and the presence of atypical observations. To tackle the challenges associated with modeling and clustering such grouped longitudinal data, we propose a finite mixture of multivariate contaminated normal linear mixed model (FM-MCNLMM) and its extended version, referred to as the EFM-MCNLMM, which allows the mixing weights to potentially depend on concomitant covariates. We develop alternating expectation conditional maximization algorithms to carry out maximum likelihood estimation for the two models. The utility and effectiveness of the proposed methodology are demonstrated through simulations and analysis of the ADNI data.