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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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    4. 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.
    5. Li, Yang & Zhao, Hui & Sun, Jianguo & Kim, KyungMann, 2014. "Nonparametric tests for panel count data with unequal observation processes," Computational Statistics & Data Analysis, Elsevier, vol. 73(C), pages 103-111.
    6. 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.
    7. 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.
    8. Kangning Wang & Xiaofei Sun, 2020. "Efficient parameter estimation and variable selection in partial linear varying coefficient quantile regression model with longitudinal data," Statistical Papers, Springer, vol. 61(3), pages 967-995, June.
    9. 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).
    10. Xiaoming Lu & Zhaozhi Fan, 2015. "Weighted quantile regression for longitudinal data," Computational Statistics, Springer, vol. 30(2), pages 569-592, June.
    11. 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.
    12. 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.
    13. 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.
    14. Geraci, Marco, 2019. "Modelling and estimation of nonlinear quantile regression with clustered data," Computational Statistics & Data Analysis, Elsevier, vol. 136(C), pages 30-46.
    15. 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).
    16. 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.
    17. 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.
    18. 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.
    19. 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.
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    21. 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.
    22. 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.

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