Composite Likelihood Inference for Simultaneous Clustering and Dimensionality Reduction of Multivariate Mixed-Type Longitudinal Data

We propose a novel multivariate hidden Markov model (HMM) designed to analyze longitudinal mixed-type data comprising continuous and ordinal variables. Our model identifies and prioritizes discriminative dimensions, i.e., those useful for clustering, while separating them from noise dimensions. By modeling variables as linear combinations of two independent latent factor sets, we achieve both parsimony and interpretability: one latent factor set represents cluster structures and evolves according to an HMM, while the other captures noise through a time-invariant multivariate normal distribution. To overcome the computational complexity of high-dimensional integrals required to compute the likelihood function, we adopt a composite likelihood approach for efficient parameter estimation. This framework enables simultaneous clustering and dimensionality reduction, offering a robust tool for analyzing complex mixed-type longitudinal datasets. The proposal is tested on simulated data by considering a large-scale simulation study and further applied to the study of lifestyle and health in the Chinese elderly population.