IDEAS home Printed from https://ideas.repec.org/a/spr/compst/v30y2015i2p569-592.html
   My bibliography  Save this article

Weighted quantile regression for longitudinal data

Author

Listed:
  • Xiaoming Lu
  • Zhaozhi Fan

Abstract

Quantile regression is a powerful statistical methodology that complements the classical linear regression by examining how covariates influence the location, scale, and shape of the entire response distribution and offering a global view of the statistical landscape. In this paper we propose a new quantile regression model for longitudinal data. The proposed approach incorporates the correlation structure between repeated measures to enhance the efficiency of the inference. In order to use the Newton–Raphson iteration method to obtain convergent estimates, the estimating functions are redefined as smoothed functions which are differentiable with respect to regression parameters. Our proposed method for quantile regression provides consistent estimates with asymptotically normal distributions. Simulation studies are carried out to evaluate the performance of the proposed method. As an illustration, the proposed method was applied to a data on the time evolution of CD4 cell numbers in HIV (human immune-deficiency virus) seroconverters and a real-life data that contains self-reported labor pain for women in two groups. Copyright Springer-Verlag Berlin Heidelberg 2015

Suggested Citation

  • Xiaoming Lu & Zhaozhi Fan, 2015. "Weighted quantile regression for longitudinal data," Computational Statistics, Springer, vol. 30(2), pages 569-592, June.
    • Handle: RePEc:spr:compst:v:30:y:2015:i:2:p:569-592
    DOI: 10.1007/s00180-014-0550-x
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/s00180-014-0550-x
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1007/s00180-014-0550-x?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. Guosheng Yin & Jianwen Cai, 2005. "Quantile Regression Models with Multivariate Failure Time Data," Biometrics, The International Biometric Society, vol. 61(1), pages 151-161, March.
    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. Sin-Ho Jung, 2003. "Rank-based regression with repeated measurements data," Biometrika, Biometrika Trust, vol. 90(3), pages 732-740, September.
    5. Liu Yuan & Bottai Matteo, 2009. "Mixed-Effects Models for Conditional Quantiles with Longitudinal Data," The International Journal of Biostatistics, De Gruyter, vol. 5(1), pages 1-24, November.
    6. Wang, Huixia & He, Xuming, 2007. "Detecting Differential Expressions in GeneChip Microarray Studies: A Quantile Approach," Journal of the American Statistical Association, American Statistical Association, vol. 102, pages 104-112, March.
    7. Xihong Lin & Raymond J. Carroll, 2006. "Semiparametric estimation in general repeated measures problems," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 68(1), pages 69-88, February.
    8. Koenker, Roger W & Bassett, Gilbert, Jr, 1978. "Regression Quantiles," Econometrica, Econometric Society, vol. 46(1), pages 33-50, January.
    9. Guosheng Yin & Joseph G. Ibrahim, 2005. "A Class of Bayesian Shared Gamma Frailty Models with Multivariate Failure Time Data," Biometrics, The International Biometric Society, vol. 61(1), pages 208-216, March.
    10. 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.
    11. 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. 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.
    2. 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.
    3. 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.
    4. 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.
    5. 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).

    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. 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.
    4. 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.
    5. 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.
    6. 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.
    7. 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).
    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. Galina Besstremyannaya & Sergei Golovan, 2023. "Measuring heterogeneity in hospital productivity: a quantile regression approach," Journal of Productivity Analysis, Springer, vol. 59(1), pages 15-43, February.
    10. Yuzhu Tian & Er’qian Li & Maozai Tian, 2016. "Bayesian joint quantile regression for mixed effects models with censoring and errors in covariates," Computational Statistics, Springer, vol. 31(3), pages 1031-1057, September.
    11. Chen, Xuerong & Tang, Niansheng & Zhou, Yong, 2016. "Quantile regression of longitudinal data with informative observation times," Journal of Multivariate Analysis, Elsevier, vol. 144(C), pages 176-188.
    12. Georges Bresson & Guy Lacroix & Mohammad Arshad Rahman, 2021. "Bayesian panel quantile regression for binary outcomes with correlated random effects: an application on crime recidivism in Canada," Empirical Economics, Springer, vol. 60(1), pages 227-259, January.
    13. Bang, Sungwan & Jhun, Myoungshic, 2012. "Simultaneous estimation and factor selection in quantile regression via adaptive sup-norm regularization," Computational Statistics & Data Analysis, Elsevier, vol. 56(4), pages 813-826.
    14. Chi-Chuan Yang & Yi-Hau Chen & Hsing-Yi Chang, 2017. "Joint regression analysis of marginal quantile and quantile association: application to longitudinal body mass index in adolescents," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 66(5), pages 1075-1090, November.
    15. Geraci, Marco, 2019. "Modelling and estimation of nonlinear quantile regression with clustered data," Computational Statistics & Data Analysis, Elsevier, vol. 136(C), pages 30-46.
    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. Ioannis Badounas & Georgios Pitselis, 2020. "Loss Reserving Estimation With Correlated Run-Off Triangles in a Quantile Longitudinal Model," Risks, MDPI, vol. 8(1), pages 1-26, February.
    18. Hanze Zhang & Yangxin Huang, 2020. "Quantile regression-based Bayesian joint modeling analysis of longitudinal–survival data, with application to an AIDS cohort study," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 26(2), pages 339-368, April.
    19. Liu Yuan & Bottai Matteo, 2009. "Mixed-Effects Models for Conditional Quantiles with Longitudinal Data," The International Journal of Biostatistics, De Gruyter, vol. 5(1), pages 1-24, November.
    20. Besstremyannaya, Galina, 2017. "Heterogeneous effect of the global financial crisis and the Great East Japan Earthquake on costs of Japanese banks," Journal of Empirical Finance, Elsevier, vol. 42(C), pages 66-89.

    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:30:y:2015:i:2:p:569-592. 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.