Sparse dynamic graphical models for longitudinal non-Gaussian data

Longitudinal non-Gaussian data are common in biomedical and microbiome studies, where responses may not be normally distributed. However, many existing dynamic graphical models are developed for Gaussian responses, while many non-Gaussian graphical models focus on cross-sectional dependence and do not explicitly estimate temporal transition effects. We propose a latent Gaussian dynamic graphical model for longitudinal non-Gaussian responses, including binary, count, and compositional outcomes. The proposed framework jointly estimates the contemporaneous conditional dependence network and the lag-one temporal dependence structure. We further develop a penalized Monte Carlo expectation maximization procedure for estimation. Simulation studies across multiple graph structures and outcome types show that the proposed method can recover both dependence structures, with more stable recovery for the lag-one temporal dependence structure and more structure-dependent recovery for the contemporaneous conditional dependence network. We apply the proposed method to longitudinal data from the Integrative Human Microbiome Project (HMP2) using a multinomial observation model. The results reveal persistent lag-one temporal dependence and contemporaneous conditional dependence among dominant microbial taxa, demonstrating the utility of the proposed framework for dynamic network analysis of longitudinal non-Gaussian biomedical data.