Partially Collapsed Gibbs Sampling for Linear Mixed-effects Models

This article presents a novel Bayesian analysis for linear mixed-effects models. The analysis is based on the method of partial collapsing that allows some components to be partially collapsed out of a model. The resulting partially collapsed Gibbs (PCG) sampler constructed to fit linear mixed-effects models is expected to exhibit much better convergence properties than the corresponding Gibbs sampler. In order to construct the PCG sampler without complicating component updates, we consider the reparameterization of model components by expressing a between-group variance in terms of a within-group variance in a linear mixed-effects model. The proposed method of partial collapsing with reparameterization is applied to the Mertons jump diffusion model as well as general linear mixed-effects models with proper prior distributions and illustrated using simulated data and longitudinal data on sleep deprivation.