Bayesian Dirichlet Regression For Correlated Compositional Outcomes.

Oregon Convention Center 

It is common to observe compositional data in various fields, with a growing interest in considering compositional data as outcomes in regression settings. The motivation for this paper stems from a study investigating the impact of sleep restriction on physical activity outcomes. The compositional outcomes were measured under both short sleep and healthy sleep conditions for the same participants. To address the dependence observed in the compositional outcomes, we introduce a Mixed-Effects Dirichlet Regression (MEDR) model. This model is designed to account for correlated outcomes arising from repeated measurements on the same subject or clustering within a group. We utilize an alternative parameterization of the Dirichlet distribution, enabling the modeling of both mean and dispersion components. Our approach offers Markov Chain Monte Carlo (MCMC) tools that are easily implementable in the programming languages Stan and R. We apply the proposed MEDR model to an experimental sleep study and illustrate its performance through simulation studies.

Compositional data, Bayesian Dirichlet regression, Markov chain Monte Carlo, physical activity, sleep restriction. 

Section on Bayesian Statistical Science