Constrained Bayesian doubly elastic net Lasso for linear quantile mixed models

Abstract

In this article, we propose a novel constrained Bayesian elastic net approach for linear quantile mixed model shrinkage. A partially collapsed Gibbs sampling algorithm is developed for efficient posterior computation based on a modified Cholesky decomposition for the covariance matrix of random effects and an asymmetric Laplace distribution for the error distribution. We demonstrate the proposed method based on simulated data and an experimental dataset from a longitudinal study of age-related macular degeneration trial. Both simulation studies and real data analysis indicate that the proposed constrained Bayesian elastic net approach is competitive with the existing methods under a variety of scenarios, such as presence of a large number of covariates and collinearity.

Keywords:

• Linear quantile mixed regression
• Cholesky decomposition
• Bayesian elastic net
• partially collapsed Gibbs sampling

Acknowledgments

We thank the editor, the associate editor and three anonymous referees for their helpful comments which led to a considerable improvement of the original manuscript.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

The first author was supported by the Scientific Research Start-up Foundation of the Civil Aviation University of China [grant number 2012QD09X]. The second author was supported by the Fundamental Research Funds for the Central Universities [grant number 3122014K013].