IDEAS home Printed from https://ideas.repec.org/a/spr/stmapp/v32y2023i1d10.1007_s10260-022-00645-2.html
   My bibliography  Save this article

A Bayesian variable selection approach to longitudinal quantile regression

Author

Listed:
  • Priya Kedia

    (JP Morgan Chase and Co.
    Indian Statistical Institute)

  • Damitri Kundu

    (Indian Statistical Institute)

  • Kiranmoy Das

    (Indian Statistical Institute)

Abstract

The literature on variable selection for mean regression is quite rich, both in the classical as well as in the Bayesian setting. However, if the goal is to assess the effects of the predictors at different levels of the response variable then quantile regression is useful. In this paper, we develop a Bayesian variable selection method for longitudinal response at some prefixed quantile levels of the response. We consider an Asymmetric Laplace Distribution (ALD) for the longitudinal response, and develop a simple Gibbs sampler algorithm for variable selection at each quantile level. We analyze a dataset from the health and retirement study (HRS) conducted by the University of Michigan for understanding the relationship between the physical health and the financial health of the aged individuals. We consider the out-of-pocket medical expenses as our response variable since it summarizes the physical and the financial well-being of an aged individual. Our proposed approach efficiently selects the important predictors at different prefixed quantile levels. Simulation studies are performed to assess the practical usefulness of the proposed approach. We also compare the performance of the proposed approach to some other existing methods of variable selection in quantile regression.

Suggested Citation

  • Priya Kedia & Damitri Kundu & Kiranmoy Das, 2023. "A Bayesian variable selection approach to longitudinal quantile regression," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 32(1), pages 149-168, March.
    • Handle: RePEc:spr:stmapp:v:32:y:2023:i:1:d:10.1007_s10260-022-00645-2
    DOI: 10.1007/s10260-022-00645-2
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10260-022-00645-2
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s10260-022-00645-2?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
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Kong, Yinfei & Li, Yujie & Zerom, Dawit, 2019. "Screening and selection for quantile regression using an alternative measure of variable importance," Journal of Multivariate Analysis, Elsevier, vol. 173(C), pages 435-455.
    2. Arnab Mukherji & Satrajit Roychoudhury & Pulak Ghosh & Sarah Brown, 2016. "Estimating Health Demand for an Aging Population: A Flexible and Robust Bayesian Joint Model," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 31(6), pages 1140-1158, September.
    3. Koenker, Roger, 2004. "Quantile regression for longitudinal data," Journal of Multivariate Analysis, Elsevier, vol. 91(1), pages 74-89, October.
    4. Fernandez, Carmen & Ley, Eduardo & Steel, Mark F. J., 2001. "Benchmark priors for Bayesian model averaging," Journal of Econometrics, Elsevier, vol. 100(2), pages 381-427, February.
    5. Jang, Woosung & Wang, Huixia Judy, 2015. "A semiparametric Bayesian approach for joint-quantile regression with clustered data," Computational Statistics & Data Analysis, Elsevier, vol. 84(C), pages 99-115.
    6. Smith, Michael & Kohn, Robert, 1996. "Nonparametric regression using Bayesian variable selection," Journal of Econometrics, Elsevier, vol. 75(2), pages 317-343, December.
    7. Brian J. Reich & Luke B. Smith, 2013. "Bayesian Quantile Regression for Censored Data," Biometrics, The International Biometric Society, vol. 69(3), pages 651-660, September.
    8. Kiranmoy Das & Pulak Ghosh & Michael J. Daniels, 2021. "Modeling Multiple Time-Varying Related Groups: A Dynamic Hierarchical Bayesian Approach With an Application to the Health and Retirement Study," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 116(534), pages 558-568, April.
    9. Dries Benoit & Rahim Alhamzawi & Keming Yu, 2013. "Bayesian lasso binary quantile regression," Computational Statistics, Springer, vol. 28(6), pages 2861-2873, December.
    10. Koenker, Roger W & Bassett, Gilbert, Jr, 1978. "Regression Quantiles," Econometrica, Econometric Society, vol. 46(1), pages 33-50, January.
    11. Park, Trevor & Casella, George, 2008. "The Bayesian Lasso," Journal of the American Statistical Association, American Statistical Association, vol. 103, pages 681-686, June.
    12. Jayabrata Biswas & Kiranmoy Das, 2021. "A Bayesian quantile regression approach to multivariate semi-continuous longitudinal data," Computational Statistics, Springer, vol. 36(1), pages 241-260, March.
    13. Xavier Sala-I-Martin & Gernot Doppelhofer & Ronald I. Miller, 2004. "Determinants of Long-Term Growth: A Bayesian Averaging of Classical Estimates (BACE) Approach," American Economic Review, American Economic Association, vol. 94(4), pages 813-835, September.
    14. Maria Marino & Alessio Farcomeni, 2015. "Linear quantile regression models for longitudinal experiments: an overview," METRON, Springer;Sapienza Università di Roma, vol. 73(2), pages 229-247, August.
    15. Taddy, Matthew A. & Kottas, Athanasios, 2010. "A Bayesian Nonparametric Approach to Inference for Quantile Regression," Journal of Business & Economic Statistics, American Statistical Association, vol. 28(3), pages 357-369.
    16. Jayabrata Biswas & Pulak Ghosh & Kiranmoy Das, 2020. "A semi-parametric quantile regression approach to zero-inflated and incomplete longitudinal outcomes," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 104(2), pages 261-283, June.
    17. Alhamzawi, Rahim & Yu, Keming, 2013. "Conjugate priors and variable selection for Bayesian quantile regression," Computational Statistics & Data Analysis, Elsevier, vol. 64(C), pages 209-219.
    18. Yun Yang & Surya T. Tokdar, 2017. "Joint Estimation of Quantile Planes Over Arbitrary Predictor Spaces," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 112(519), pages 1107-1120, 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. Alhamzawi, Rahim, 2016. "Bayesian model selection in ordinal quantile regression," Computational Statistics & Data Analysis, Elsevier, vol. 103(C), pages 68-78.
    2. Ali Aghamohammadi, 2018. "Bayesian analysis of dynamic panel data by penalized quantile regression," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 27(1), pages 91-108, March.
    3. Jayabrata Biswas & Kiranmoy Das, 2021. "A Bayesian quantile regression approach to multivariate semi-continuous longitudinal data," Computational Statistics, Springer, vol. 36(1), pages 241-260, March.
    4. Kiranmoy Das & Bhuvanesh Pareek & Sarah Brown & Pulak Ghosh, 2022. "A semi-parametric Bayesian dynamic hurdle model with an application to the health and retirement study," Computational Statistics, Springer, vol. 37(2), pages 837-863, April.
    5. Fabrizi, Enrico & Salvati, Nicola & Trivisano, Carlo, 2020. "Robust Bayesian small area estimation based on quantile regression," Computational Statistics & Data Analysis, Elsevier, vol. 145(C).
    6. Ji, Yonggang & Lin, Nan & Zhang, Baoxue, 2012. "Model selection in binary and tobit quantile regression using the Gibbs sampler," Computational Statistics & Data Analysis, Elsevier, vol. 56(4), pages 827-839.
    7. Dries Benoit & Rahim Alhamzawi & Keming Yu, 2013. "Bayesian lasso binary quantile regression," Computational Statistics, Springer, vol. 28(6), pages 2861-2873, December.
    8. Seongil Jo & Taeyoung Roh & Taeryon Choi, 2016. "Bayesian spectral analysis models for quantile regression with Dirichlet process mixtures," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 28(1), pages 177-206, March.
    9. Paolo Frumento & Nicola Salvati, 2021. "Parametric modeling of quantile regression coefficient functions with count data," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 30(4), pages 1237-1258, October.
    10. Gilles Dufrenot & Valerie Mignon & Charalambos Tsangarides, 2010. "The trade-growth nexus in the developing countries: a quantile regression approach," Review of World Economics (Weltwirtschaftliches Archiv), Springer;Institut für Weltwirtschaft (Kiel Institute for the World Economy), vol. 146(4), pages 731-761, December.
    11. Sweata Sen & Damitri Kundu & Kiranmoy Das, 2023. "Variable selection for categorical response: a comparative study," Computational Statistics, Springer, vol. 38(2), pages 809-826, June.
    12. Rodrigues, T. & Dortet-Bernadet, J.-L. & Fan, Y., 2019. "Simultaneous fitting of Bayesian penalised quantile splines," Computational Statistics & Data Analysis, Elsevier, vol. 134(C), pages 93-109.
    13. Jayabrata Biswas & Pulak Ghosh & Kiranmoy Das, 2020. "A semi-parametric quantile regression approach to zero-inflated and incomplete longitudinal outcomes," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 104(2), pages 261-283, June.
    14. Mai Dao & Min Wang & Souparno Ghosh & Keying Ye, 2022. "Bayesian variable selection and estimation in quantile regression using a quantile-specific prior," Computational Statistics, Springer, vol. 37(3), pages 1339-1368, July.
    15. Hemant Kulkarni & Jayabrata Biswas & Kiranmoy Das, 2019. "A joint quantile regression model for multiple longitudinal outcomes," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 103(4), pages 453-473, December.
    16. Yingying Hu & Huixia Judy Wang & Xuming He & Jianhua Guo, 2021. "Bayesian joint-quantile regression," Computational Statistics, Springer, vol. 36(3), pages 2033-2053, September.
    17. Henry R. Scharf & Xinyi Lu & Perry J. Williams & Mevin B. Hooten, 2022. "Constructing Flexible, Identifiable and Interpretable Statistical Models for Binary Data," International Statistical Review, International Statistical Institute, vol. 90(2), pages 328-345, August.
    18. Jose E. Gomez-Gonzalez & Jorge M. Uribe & Oscar M. Valencia, 2024. "Asymmetric Sovereign Risk: Implications for Climate Change Preparation," IREA Working Papers 202401, University of Barcelona, Research Institute of Applied Economics, revised Jan 2024.
    19. Elisabeth Waldmann & Thomas Kneib & Yu Ryan Yu & Stefan Lang, 2012. "Bayesian semiparametric additive quantile regression," Working Papers 2012-06, Faculty of Economics and Statistics, Universität Innsbruck.
    20. Gilles Celeux & Mohammed El Anbari & Jean-Michel Marin & Christian P. Robert, 2010. "Regularization in Regression : Comparing Bayesian and Frequentist Methods in a Poorly Informative Situation," Working Papers 2010-43, Center for Research in Economics and 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:spr:stmapp:v:32:y:2023:i:1:d:10.1007_s10260-022-00645-2. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    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.