Fast Bayesian inference in a class of sparse linear mixed effects models

TL;DR

This paper introduces a fast variational Bayes inference method for sparse linear mixed effects models with Bayesian variable selection, applicable to large datasets and extended to skew-t errors, demonstrated through simulations and real data.

Contribution

It develops a scalable variational Bayes algorithm for Bayesian variable selection in mixed effects models, including an EM approach with Occam's window for normal errors and extension to skew-t errors.

Findings

Algorithm performs well in simulation studies.

Effective in modeling longitudinal athlete performance.

Applicable to large datasets with complex error structures.

Abstract

Linear mixed effects models are widely used in statistical modelling. We consider a mixed effects model with Bayesian variable selection in the random effects using spike-and-slab priors and developed a variational Bayes inference scheme that can be applied to large data sets. An EM algorithm is proposed for the model with normal errors where the posterior distribution of the variable inclusion parameters is approximated using an Occam's window approach. Placing this approach within a variational Bayes scheme also the algorithm to be extended to the model with skew-t errors. The performance of the algorithm is evaluated in a simulation study and applied to a longitudinal model for elite athlete performance in the 100 metre sprint and weightlifting.