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

Yonggang Ji1, Haifang Shi1

  • 1School of Science, Civil Aviation University of China, Tianjin, China.

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This study introduces Bayesian methods for quantile regression, enhancing variable selection in mixed models. The approach improves statistical analysis for complex datasets, offering robust insights into data distributions.

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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.