IDEAS home Printed from https://ideas.repec.org/a/plo/pone00/0283100.html
   My bibliography  Save this article

Study of Bayesian variable selection method on mixed linear regression models

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: https://journals.plos.org/plosone/article?id=10.1371/journal.pone.0283100
    Download Restriction: no

    File URL: https://journals.plos.org/plosone/article/file?id=10.1371/journal.pone.0283100&type=printable
    Download Restriction: no

    File URL: https://libkey.io/10.1371/journal.pone.0283100?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    References listed on IDEAS

    as
    1. 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.
    2. 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.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Haili Zhang & Guohua Zou, 2020. "Cross-Validation Model Averaging for Generalized Functional Linear Model," Econometrics, MDPI, vol. 8(1), pages 1-35, February.
    2. Matthew Gentzkow & Jesse M. Shapiro & Matt Taddy, 2019. "Measuring Group Differences in High‐Dimensional Choices: Method and Application to Congressional Speech," Econometrica, Econometric Society, vol. 87(4), pages 1307-1340, July.
    3. D. Calvetti & E. Somersalo, 2025. "Distributed Tikhonov regularization for ill-posed inverse problems from a Bayesian perspective," Computational Optimization and Applications, Springer, vol. 91(2), pages 541-572, June.
    4. Ziwen Gao & Jiahui Zou & Xinyu Zhang & Yanyuan Ma, 2023. "Frequentist model averaging for envelope models," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 50(3), pages 1325-1364, September.
    5. Canhong Wen & Xueqin Wang & Shaoli Wang, 2015. "Laplace Error Penalty-based Variable Selection in High Dimension," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 42(3), pages 685-700, September.
    6. Hollstein, Fabian & Prokopczuk, Marcel & Tharann, Björn & Wese Simen, Chardin, 2025. "Predicting the equity premium around the globe: Comprehensive evidence from a large sample," International Journal of Forecasting, Elsevier, vol. 41(1), pages 208-228.
    7. Shangwei Zhao & Jun Liao & Dalei Yu, 2020. "Model averaging estimator in ridge regression and its large sample properties," Statistical Papers, Springer, vol. 61(4), pages 1719-1739, August.
    8. Mogliani, Matteo & Simoni, Anna, 2021. "Bayesian MIDAS penalized regressions: Estimation, selection, and prediction," Journal of Econometrics, Elsevier, vol. 222(1), pages 833-860.
    9. Hollstein, Fabian & Prokopczuk, Marcel & Tharann, Björn & Wese Simen, Chardin, 2021. "Predictability in commodity markets: Evidence from more than a century," Journal of Commodity Markets, Elsevier, vol. 24(C).
    10. Mallick, Himel & Yi, Nengjun, 2017. "Bayesian group bridge for bi-level variable selection," Computational Statistics & Data Analysis, Elsevier, vol. 110(C), pages 115-133.
    11. Posch, Konstantin & Arbeiter, Maximilian & Pilz, Juergen, 2020. "A novel Bayesian approach for variable selection in linear regression models," Computational Statistics & Data Analysis, Elsevier, vol. 144(C).
    12. Dimitris Korobilis & Kenichi Shimizu, 2022. "Bayesian Approaches to Shrinkage and Sparse Estimation," Foundations and Trends(R) in Econometrics, now publishers, vol. 11(4), pages 230-354, June.
    13. Chowdhury, K.P., 2023. "Nonparametric functional analysis under joint estimation with applications to identifying highly cited papers," Journal of Informetrics, Elsevier, vol. 17(4).
    14. Ando, Tomohiro & Bai, Jushan & Li, Kunpeng, 2022. "Bayesian and maximum likelihood analysis of large-scale panel choice models with unobserved heterogeneity," Journal of Econometrics, Elsevier, vol. 230(1), pages 20-38.
    15. Zhang, Yaojie & Wahab, M.I.M. & Wang, Yudong, 2023. "Forecasting crude oil market volatility using variable selection and common factor," International Journal of Forecasting, Elsevier, vol. 39(1), pages 486-502.
    16. Xianyi Wu & Xian Zhou, 2019. "On Hodges’ superefficiency and merits of oracle property in model selection," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 71(5), pages 1093-1119, October.
    17. Sakae Oya, 2021. "A Bayesian Graphical Approach for Large-Scale Portfolio Management with Fewer Historical Data," Papers 2103.05880, arXiv.org, revised Mar 2022.
    18. Shi, Qi, 2025. "Technical indicators and aggregate stock returns: An updated look," Journal of Multinational Financial Management, Elsevier, vol. 77(C).
    19. Feng, Xiangnan & Lu, Bin & Song, Xinyuan & Ma, Shuang, 2019. "Financial literacy and household finances: A Bayesian two-part latent variable modeling approach," Journal of Empirical Finance, Elsevier, vol. 51(C), pages 119-137.
    20. Zangin Zeebari & Kristofer Månsson & Pär Sjölander & Magnus Söderberg, 2023. "Regularized conditional estimators of unit inefficiency in stochastic frontier analysis, with application to electricity distribution market," Journal of Productivity Analysis, Springer, vol. 59(1), pages 79-97, February.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:plo:pone00:0283100. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: plosone (email available below). General contact details of provider: https://journals.plos.org/plosone/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.