Bayesian Inference on the Impact of Serious Life Events on Insomnia and Obesity

We investigate the impact of significant life events on two critical health outcomes: insomnia and obesity. Using data from the Household, Income, and Labour Dynamics in Australia (HILDA) survey, we focus on significant life events experienced in the preceding 12 months. To model these health outcomes jointly, we employ a bivariate random effects probit panel data model and a longitudinal random effects panel data model whose outcomes can be a combination of discrete/categorical and continuous variables. Estimating these random effects panel data models is challenging because the likelihood is an integral over the latent individual random effects. In addition, the models often have a large number of predictors. In this paper, Bayesian inference is carried out using a particle Metropolis within a Gibbs sampler, which is particularly well suited for statistical models with latent variables. Additionally, within this inference framework, we integrate a Hamiltonian Monte Carlo (HMC) step to sample the high-dimensional vector of regression coefficients efficiently. The HMC step enables faster convergence and improved mixing of the Markov chain. Our article contributes to a better understanding of how stress-related life events shape health outcomes and demonstrates the advantages of combining particle Metropolis within Gibbs and HMC in the estimation of complex panel data models.