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Quantile regression for longitudinal data with a working correlation model

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  • Fu, Liya
  • Wang, You-Gan

Abstract

This paper proposes a linear quantile regression analysis method for longitudinal data that combines the between- and within-subject estimating functions, which incorporates the correlations between repeated measurements. Therefore, the proposed method results in more efficient parameter estimation relative to the estimating functions based on an independence working model. To reduce computational burdens, the induced smoothing method is introduced to obtain parameter estimates and their variances. Under some regularity conditions, the estimators derived by the induced smoothing method are consistent and have asymptotically normal distributions. A number of simulation studies are carried out to evaluate the performance of the proposed method. The results indicate that the efficiency gain for the proposed method is substantial especially when strong within correlations exist. Finally, a dataset from the audiology growth research is used to illustrate the proposed methodology.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:csdana:v:56:y:2012:i:8:p:2526-2538
    DOI: 10.1016/j.csda.2012.02.005
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    Cited by:

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    3. 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.
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    5. Geraci, Marco, 2019. "Modelling and estimation of nonlinear quantile regression with clustered data," Computational Statistics & Data Analysis, Elsevier, vol. 136(C), pages 30-46.
    6. Weihua Zhao & Weiping Zhang & Heng Lian, 2020. "Marginal quantile regression for varying coefficient models with longitudinal data," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 72(1), pages 213-234, February.
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    8. Zhao, Weihua & Lian, Heng & Song, Xinyuan, 2017. "Composite quantile regression for correlated data," Computational Statistics & Data Analysis, Elsevier, vol. 109(C), pages 15-33.
    9. 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.
    10. Xiaoming Lu & Zhaozhi Fan, 2015. "Weighted quantile regression for longitudinal data," Computational Statistics, Springer, vol. 30(2), pages 569-592, June.
    11. 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.
    12. 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.
    13. 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).
    14. Yujing Shao & Lei Wang, 2022. "Generalized partial linear models with nonignorable dropouts," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 85(2), pages 223-252, February.
    15. Christian E. Galarza & Luis M. Castro & Francisco Louzada & Victor H. Lachos, 2020. "Quantile regression for nonlinear mixed effects models: a likelihood based perspective," Statistical Papers, Springer, vol. 61(3), pages 1281-1307, June.
    16. 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.
    17. 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).
    18. Lei Wang & Wei Ma, 2021. "Improved empirical likelihood inference and variable selection for generalized linear models with longitudinal nonignorable dropouts," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 73(3), pages 623-647, June.
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    21. 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.
    22. Yuan Xue & Xiangrong Yin, 2015. "Sufficient dimension folding for a functional of conditional distribution of matrix- or array-valued objects," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 27(2), pages 253-269, June.

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