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Study of Bayesian variable selection method on mixed linear regression models

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  • Yong Li
  • Hefei Liu
  • Rubing Li

Abstract

Variable selection has always been an important issue in statistics. When a linear regression model is used to fit data, selecting appropriate explanatory variables that strongly impact the response variables has a significant effect on the model prediction accuracy and interpretation effect. redThis study introduces the Bayesian adaptive group Lasso method to solve the variable selection problem under a mixed linear regression model with a hidden state and explanatory variables with a grouping structure. First, the definition of the implicit state mixed linear regression model is presented. Thereafter, the Bayesian adaptive group Lasso method is used to determine the penalty function and parameters, after which each parameter’s specific form of the fully conditional posterior distribution is calculated. Moreover, the Gibbs algorithm design is outlined. Simulation experiments are conducted to compare the variable selection and parameter estimation effects in different states. Finally, a dataset of Alzheimer’s Disease is used for application analysis. The results demonstrate that the proposed method can identify the observation from different hidden states, but the results of the variable selection in different states are obviously different.

Suggested Citation

  • Yong Li & Hefei Liu & Rubing Li, 2023. "Study of Bayesian variable selection method on mixed linear regression models," PLOS ONE, Public Library of Science, vol. 18(3), pages 1-13, March.
    • Handle: RePEc:plo:pone00:0283100
    DOI: 10.1371/journal.pone.0283100
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    References listed on IDEAS

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    1. Wang, Hansheng & Leng, Chenlei, 2008. "A note on adaptive group lasso," Computational Statistics & Data Analysis, Elsevier, vol. 52(12), pages 5277-5286, August.
    2. Liu, Hefei & Song, Xinyuan & Zhang, Baoxue, 2022. "Varying-coefficient hidden Markov models with zero-effect regions," Computational Statistics & Data Analysis, Elsevier, vol. 173(C).
    3. Chenlei Leng & Minh-Ngoc Tran & David Nott, 2014. "Bayesian adaptive Lasso," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 66(2), pages 221-244, April.
    4. Cheryl J. Flynn & Clifford M. Hurvich & Jeffrey S. Simonoff, 2013. "Efficiency for Regularization Parameter Selection in Penalized Likelihood Estimation of Misspecified Models," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 108(503), pages 1031-1043, September.
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