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 longitu-dinal mixed-type data comprising continuous and ordinal variables. Our model identifies andprioritizes discriminative dimensions, i.e., those useful for clustering, while separating themfrom noise dimensions. By modeling variables as linear combinations of two independentlatent factor sets, we achieve both parsimony and interpretability: one latent factor set rep-resents cluster structures and evolves according to an HMM, while the other captures noisethrough a time-invariant multivariate normal distribution. To overcome the computationalcomplexity of high-dimensional integrals required to compute the likelihood function, weadopt a composite likelihood approach for efficient parameter estimation. This frameworkenables simultaneous clustering and dimensionality reduction, offering a robust tool for ana-lyzing complex mixed-type longitudinal datasets. The proposal is tested on simulated databy considering a large-scale simulation study and further applied to the study of lifestyle andhealth in the Chinese elderly population.