A Latent Class Bayesian Model for Multivariate Longitudinal Outcomes with Excess Zeros

Latent class models have been successfully used to handle complex datasets in
different disciplines. For longitudinal outcomes, we often get a trajectory of the outcome for each individual, and on that basis, we cluster them for a powerful statistical
inference. Latent class models have been used to handle multivariate longitudinal
outcomes coming from biology, health sciences, and economics. In this paper, we
propose a Bayesian latent class model for multivariate outcomes with excess zeros.
We consider a Tobit model for zero-inflated continuous outcomes such as out-of-pocket
medical expenses (OOPME), a two-part model for financial debt, and a ZIP model
for counting outcomes with excess zeros. We develop a Bayesian mixture model and
employ an adaptive Lasso-type shrinkage method for variable selection. We analyze
data from the Health and Retirement Study conducted by the University of Michigan
and consider modeling four important outcomes measuring the physical and financial health of the aged individuals. Our analysis detects several latent clusters for
different outcomes. Practical usefulness of the proposed model is validated through
a simulation study.