Bayesian parsimonious covariance estimation for hierarchical linear mixed models

We consider a non-centered parameterization of the standard random-effects model, which is based on the Cholesky decomposition of the variance-covariance matrix. The regression type structure of the non-centered parameterization allows us to use Bayesian variable selection methods for covariance selection. We search for a parsimonious variance-covariance matrix by identifying the non-zero elements of the Cholesky factors. With this method we are able to learn from the data for each effect whether it is random or not, and whether covariances among random effects are zero. An application in marketing shows a substantial reduction of the number of free elements in the variance-covariance matrix.