Bayesian variable selection in linear quantile mixed models for longitudinal data with application to macular...

Area of Science:

• Statistics
• Biostatistics
• Econometrics

Background:

• Linear mixed models are widely used but often assume normal distributions.
• Quantile regression offers a more comprehensive view of data by modeling conditional quantiles.
• Bayesian methods provide a flexible framework for complex statistical modeling.

Purpose of the Study:

• To develop a Bayesian framework for quantile regression in linear mixed models.
• To introduce novel variable selection techniques for both fixed and random effects.
• To enhance computational efficiency through a partially collapsed Gibbs sampling algorithm.

Main Methods:

• Bayesian analysis of linear mixed models for quantile regression.
• Cholesky decomposition for the covariance matrix of random effects.
• Bayesian adaptive lasso and extended Bayesian adaptive group lasso for variable selection.
• Spike and slab priors for variable selection.
• Partially collapsed Gibbs sampling for posterior inference.

Main Results:

• The proposed Bayesian shrinkage approach effectively performs variable selection for fixed and random effects.
• The developed Gibbs sampling algorithm improves Markov chain mixing for posterior inference.
• The methods were validated through simulation experiments and application to real-world data.

Conclusions:

• The novel Bayesian methods provide a powerful tool for analyzing complex data using quantile mixed regression.
• The variable selection procedures enhance model interpretability and predictive accuracy.
• The efficient sampling algorithm facilitates practical application of these advanced statistical techniques.