IDEAS home Printed from https://ideas.repec.org/a/bla/biomet/v77y2021i2p391-400.html
   My bibliography  Save this article

Bayesian group selection in logistic regression with application to MRI data analysis

Author

Listed:
  • Kyoungjae Lee
  • Xuan Cao

Abstract

We consider Bayesian logistic regression models with group‐structured covariates. In high‐dimensional settings, it is often assumed that only a small portion of groups are significant, and thus, consistent group selection is of significant importance. While consistent frequentist group selection methods have been proposed, theoretical properties of Bayesian group selection methods for logistic regression models have not been investigated yet. In this paper, we consider a hierarchical group spike and slab prior for logistic regression models in high‐dimensional settings. Under mild conditions, we establish strong group selection consistency of the induced posterior, which is the first theoretical result in the Bayesian literature. Through simulation studies, we demonstrate that the proposed method outperforms existing state‐of‐the‐art methods in various settings. We further apply our method to a magnetic resonance imaging data set for predicting Parkinson's disease and show its benefits over other contenders.

Suggested Citation

  • Kyoungjae Lee & Xuan Cao, 2021. "Bayesian group selection in logistic regression with application to MRI data analysis," Biometrics, The International Biometric Society, vol. 77(2), pages 391-400, June.
    • Handle: RePEc:bla:biomet:v:77:y:2021:i:2:p:391-400
    DOI: 10.1111/biom.13290
    as

    Download full text from publisher

    File URL: https://doi.org/10.1111/biom.13290
    Download Restriction: no
    File URL: https://libkey.io/10.1111/biom.13290?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. Lukas Meier & Sara Van De Geer & Peter Bühlmann, 2008. "The group lasso for logistic regression," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 70(1), pages 53-71, February.
    2. Sean M. O'Brien & David B. Dunson, 2004. "Bayesian Multivariate Logistic Regression," Biometrics, The International Biometric Society, vol. 60(3), pages 739-746, September.
    3. Howard D. Bondell & Brian J. Reich, 2012. "Consistent High-Dimensional Bayesian Variable Selection via Penalized Credible Regions," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 107(500), pages 1610-1624, December.
    4. Naveen N. Narisetty & Juan Shen & Xuming He, 2019. "Skinny Gibbs: A Consistent and Scalable Gibbs Sampler for Model Selection," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 114(527), pages 1205-1217, July.
    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. Gabriel E Hoffman & Benjamin A Logsdon & Jason G Mezey, 2013. "PUMA: A Unified Framework for Penalized Multiple Regression Analysis of GWAS Data," PLOS Computational Biology, Public Library of Science, vol. 9(6), pages 1-19, June.
    2. Tutz, Gerhard & Pößnecker, Wolfgang & Uhlmann, Lorenz, 2015. "Variable selection in general multinomial logit models," Computational Statistics & Data Analysis, Elsevier, vol. 82(C), pages 207-222.
    3. Ye, Ya-Fen & Shao, Yuan-Hai & Deng, Nai-Yang & Li, Chun-Na & Hua, Xiang-Yu, 2017. "Robust Lp-norm least squares support vector regression with feature selection," Applied Mathematics and Computation, Elsevier, vol. 305(C), pages 32-52.
    4. Vincent, Martin & Hansen, Niels Richard, 2014. "Sparse group lasso and high dimensional multinomial classification," Computational Statistics & Data Analysis, Elsevier, vol. 71(C), pages 771-786.
    5. Haoying Wang & Guohui Wu, 2022. "Modeling discrete choices with large fine-scale spatial data: opportunities and challenges," Journal of Geographical Systems, Springer, vol. 24(3), pages 325-351, July.
    6. Croux, Christophe & Jagtiani, Julapa & Korivi, Tarunsai & Vulanovic, Milos, 2020. "Important factors determining Fintech loan default: Evidence from a lendingclub consumer platform," Journal of Economic Behavior & Organization, Elsevier, vol. 173(C), pages 270-296.
    7. Caner, Mehmet, 2023. "Generalized linear models with structured sparsity estimators," Journal of Econometrics, Elsevier, vol. 236(2).
    8. repec:jss:jstsof:33:i01 is not listed on IDEAS
    9. Bilin Zeng & Xuerong Meggie Wen & Lixing Zhu, 2017. "A link-free sparse group variable selection method for single-index model," Journal of Applied Statistics, Taylor & Francis Journals, vol. 44(13), pages 2388-2400, October.
    10. Ander Wilson & Brian J. Reich, 2014. "Confounder selection via penalized credible regions," Biometrics, The International Biometric Society, vol. 70(4), pages 852-861, December.
    11. Constandina Koki & Loukia Meligkotsidou & Ioannis Vrontos, 2020. "Forecasting under model uncertainty: Non‐homogeneous hidden Markov models with Pòlya‐Gamma data augmentation," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 39(4), pages 580-598, July.
    12. Olga Klopp & Marianna Pensky, 2013. "Sparse High-dimensional Varying Coefficient Model : Non-asymptotic Minimax Study," Working Papers 2013-30, Center for Research in Economics and Statistics.
    13. Jiang, Cuixia & Xiong, Wei & Xu, Qifa & Liu, Yezheng, 2021. "Predicting default of listed companies in mainland China via U-MIDAS Logit model with group lasso penalty," Finance Research Letters, Elsevier, vol. 38(C).
    14. Li, Peili & Jiao, Yuling & Lu, Xiliang & Kang, Lican, 2022. "A data-driven line search rule for support recovery in high-dimensional data analysis," Computational Statistics & Data Analysis, Elsevier, vol. 174(C).
    15. Osamu Komori & Shinto Eguchi & John B. Copas, 2015. "Generalized t-statistic for two-group classification," Biometrics, The International Biometric Society, vol. 71(2), pages 404-416, June.
    16. Wei, Fengrong & Zhu, Hongxiao, 2012. "Group coordinate descent algorithms for nonconvex penalized regression," Computational Statistics & Data Analysis, Elsevier, vol. 56(2), pages 316-326.
    17. Luu, Tung Duy & Fadili, Jalal & Chesneau, Christophe, 2019. "PAC-Bayesian risk bounds for group-analysis sparse regression by exponential weighting," Journal of Multivariate Analysis, Elsevier, vol. 171(C), pages 209-233.
    18. Yang, Yanlin & Hu, Xuemei & Jiang, Huifeng, 2022. "Group penalized logistic regressions predict up and down trends for stock prices," The North American Journal of Economics and Finance, Elsevier, vol. 59(C).
    19. Zeng, Yaohui & Yang, Tianbao & Breheny, Patrick, 2021. "Hybrid safe–strong rules for efficient optimization in lasso-type problems," Computational Statistics & Data Analysis, Elsevier, vol. 153(C).
    20. Lee, In Gyu & Yoon, Sang Won & Won, Daehan, 2022. "A Mixed Integer Linear Programming Support Vector Machine for Cost-Effective Group Feature Selection: Branch-Cut-and-Price Approach," European Journal of Operational Research, Elsevier, vol. 299(3), pages 1055-1068.
    21. Ruidi Chen & Ioannis Ch. Paschalidis, 2022. "Robust Grouped Variable Selection Using Distributionally Robust Optimization," Journal of Optimization Theory and Applications, Springer, vol. 194(3), pages 1042-1071, September.

    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:bla:biomet:v:77:y:2021:i:2:p:391-400. 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: Wiley Content Delivery (email available below). General contact details of provider: http://www.blackwellpublishing.com/journal.asp?ref=0006-341X .

    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.