IDEAS home Printed from https://ideas.repec.org/a/spr/compst/v39y2024i2d10.1007_s00180-022-01318-0.html

Distributed quantile regression for longitudinal big data

Author

Listed:
  • Ye Fan

    (Capital University of Economics and Business)

  • Nan Lin

    (Washington University in St. Louis)

  • Liqun Yu

    (Washington University in St. Louis)

Abstract

Longitudinal data, measurements taken from the same subjects over time, appear routinely in many scientific fields, such as biomedical science, public health, ecology and environmental sciences. With the rapid development of information technology, modern longitudinal data are becoming massive in volume and high dimensional, hence often require distributed analysis in real-world applications. Standard divide-and-conquer techniques do not apply directly to longitudinal big data due to within-subject dependence. In this paper, we focus on developing a distributed algorithm to support quantile regression (QR) analysis of longitudinal big data, which currently remains an open and challenging issue. We employ weighted quantile regression (WQR) to accommodate the correlation in longitudinal big data, and parallelize the WQR estimation process with a two-stage algorithm to support distributed computing. Based on weights estimated in the first stage by the Newton–Raphson algorithm, the second stage solves the WQR problem using the multi-block alternating direction method of multipliers (ADMM). Simulation studies show that, compared to traditional non-distributed algorithms, our proposed method has favorable estimation accuracy and is computationally more efficient in both non-distributed and distributed environments. Further, we also analyze an air quality data set to illustrate the practical performance of this method.

Suggested Citation

  • Ye Fan & Nan Lin & Liqun Yu, 2024. "Distributed quantile regression for longitudinal big data," Computational Statistics, Springer, vol. 39(2), pages 751-779, April.
    • Handle: RePEc:spr:compst:v:39:y:2024:i:2:d:10.1007_s00180-022-01318-0
    DOI: 10.1007/s00180-022-01318-0
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s00180-022-01318-0
    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/s00180-022-01318-0?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

    for a different version of it.

    References listed on IDEAS

    as
    1. Liqun Yu & Nan Lin, 2017. "ADMM for Penalized Quantile Regression in Big Data," International Statistical Review, International Statistical Institute, vol. 85(3), pages 494-518, December.
    2. Koenker, Roger, 2004. "Quantile regression for longitudinal data," Journal of Multivariate Analysis, Elsevier, vol. 91(1), pages 74-89, October.
    3. B. M. Brown & You-Gan Wang, 2005. "Standard errors and covariance matrices for smoothed rank estimators," Biometrika, Biometrika Trust, vol. 92(1), pages 149-158, March.
    4. Koenker, Roger W & Bassett, Gilbert, Jr, 1978. "Regression Quantiles," Econometrica, Econometric Society, vol. 46(1), pages 33-50, January.
    5. Chen, Lanjue & Zhou, Yong, 2020. "Quantile regression in big data: A divide and conquer based strategy," Computational Statistics & Data Analysis, Elsevier, vol. 144(C).
    6. Fu, Liya & Wang, You-Gan, 2012. "Quantile regression for longitudinal data with a working correlation model," Computational Statistics & Data Analysis, Elsevier, vol. 56(8), pages 2526-2538.
    7. 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.
    8. Haiying Wang & Yanyuan Ma, 2021. "Optimal subsampling for quantile regression in big data," Biometrika, Biometrika Trust, vol. 108(1), pages 99-112.
    9. Zhao, Weihua & Lian, Heng & Song, Xinyuan, 2017. "Composite quantile regression for correlated data," Computational Statistics & Data Analysis, Elsevier, vol. 109(C), pages 15-33.
    10. Cheng Yong Tang & Chenlei Leng, 2011. "Empirical likelihood and quantile regression in longitudinal data analysis," Biometrika, Biometrika Trust, vol. 98(4), pages 1001-1006.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Shanshan Wang & Wei Cao & Xiaoxue Hu & Hanyu Zhong & Weixi Sun, 2025. "A Selective Overview of Quantile Regression for Large-Scale Data," Mathematics, MDPI, vol. 13(5), pages 1-30, March.
    2. Zou, Hang & Jiang, Yunlu, 2026. "Communication-efficient distributed robust variable selection for heterogeneous massive data," Statistics & Probability Letters, Elsevier, vol. 228(C).

    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. 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.
    2. Fu, Liya & Wang, You-Gan, 2016. "Efficient parameter estimation via Gaussian copulas for quantile regression with longitudinal data," Journal of Multivariate Analysis, Elsevier, vol. 143(C), pages 492-502.
    3. Xiaoming Lu & Zhaozhi Fan, 2015. "Weighted quantile regression for longitudinal data," Computational Statistics, Springer, vol. 30(2), pages 569-592, June.
    4. Fu, Liya & Wang, You-Gan & Zhu, Min, 2015. "A Gaussian pseudolikelihood approach for quantile regression with repeated measurements," Computational Statistics & Data Analysis, Elsevier, vol. 84(C), pages 41-53.
    5. Jing Lv & Chaohui Guo, 2017. "Efficient parameter estimation via modified Cholesky decomposition for quantile regression with longitudinal data," Computational Statistics, Springer, vol. 32(3), pages 947-975, September.
    6. Lin, Fangzheng & Tang, Yanlin & Zhu, Zhongyi, 2020. "Weighted quantile regression in varying-coefficient model with longitudinal data," Computational Statistics & Data Analysis, Elsevier, vol. 145(C).
    7. Geraci, Marco, 2019. "Modelling and estimation of nonlinear quantile regression with clustered data," Computational Statistics & Data Analysis, Elsevier, vol. 136(C), pages 30-46.
    8. 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.
    9. Xiaoming Lu & Zhaozhi Fan, 2020. "Generalized linear mixed quantile regression with panel data," PLOS ONE, Public Library of Science, vol. 15(8), pages 1-16, August.
    10. Fan, Ye & Lin, Nan, 2025. "Sequential quantile regression for stream data by least squares," Journal of Econometrics, Elsevier, vol. 249(PA).
    11. Gomez-Gonzalez, Jose E. & Uribe, Jorge M. & Valencia, Oscar M., 2025. "Asymmetric sovereign risk: Implications for climate change preparation," World Development, Elsevier, vol. 188(C).
    12. Merlo, Luca & Petrella, Lea & Salvati, Nicola & Tzavidis, Nikos, 2022. "Marginal M-quantile regression for multivariate dependent data," Computational Statistics & Data Analysis, Elsevier, vol. 173(C).
    13. 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.
    14. Francesco Schirripa Spagnolo & Nicola Salvati & Antonella D’Agostino & Ides Nicaise, 2020. "The use of sampling weights in M‐quantile random‐effects regression: an application to Programme for International Student Assessment mathematics scores," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 69(4), pages 991-1012, August.
    15. Suthakaran Ratnasingam & Ramadha D. Piyadi Gamage, 2025. "Empirical likelihood change point detection in quantile regression models," Computational Statistics, Springer, vol. 40(2), pages 999-1020, February.
    16. Hyunkeun Ryan Cho, 2018. "Statistical inference in a growth curve quantile regression model for longitudinal data," Biometrics, The International Biometric Society, vol. 74(3), pages 855-862, September.
    17. Petrella, Lea & Raponi, Valentina, 2019. "Joint estimation of conditional quantiles in multivariate linear regression models with an application to financial distress," Journal of Multivariate Analysis, Elsevier, vol. 173(C), pages 70-84.
    18. Fu, Liya & Wang, You-Gan, 2012. "Quantile regression for longitudinal data with a working correlation model," Computational Statistics & Data Analysis, Elsevier, vol. 56(8), pages 2526-2538.
    19. Wang, Kangning & Li, Shaomin & Zhang, Benle, 2021. "Robust communication-efficient distributed composite quantile regression and variable selection for massive data," Computational Statistics & Data Analysis, Elsevier, vol. 161(C).
    20. Lv, Jing & Guo, Chaohui & Yang, Hu & Li, Yalian, 2017. "A moving average Cholesky factor model in covariance modeling for composite quantile regression with longitudinal data," Computational Statistics & Data Analysis, Elsevier, vol. 112(C), pages 129-144.

    More about this item

    Keywords

    ;
    ;
    ;
    ;
    ;

    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:spr:compst:v:39:y:2024:i:2:d:10.1007_s00180-022-01318-0. 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.