Bayesian variable selection in linear mixed effects models

Abstract: Variable selection techniques have been well researched and used in many different fields. There is rich literature on Bayesian variable selection in linear regression models, but only few of them are about mixed effects. The topic of the thesis is Bayesian variable selection in linear mixed effect models. The choice of methods to achieve this goal is to induce different shrinkage priors. Both unimodal shrinkage priors and spike-and-slab priors are used and compared. The distributions that have been chosen, either as unimodal priors or parts of the spike-and-slab priors are the Normal distribution, the Student-t distribution and the Laplace distribution. Both the simulations and the real dataset studies have been carried out, with the intention of investigating and evaluating how good the chosen distributions are as shrinkage priors. Obtained results from the real dataset shows that spike-and-slab priors yield more shrinkage effect than what unimodal priors does. However, inducing spike-and-slab priors carelessly without any consideration if the size of the data is sufficiently large enough may lead to poor model parameter estimations. Results from the simulations studies indicates that a mixture of Laplace distribution for both the spike and slab components is the prior that yields the highest shrinkage effect among the investigated shrinkage priors.