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Quantile regression for longitudinal data with a working correlation model

  • Fu, Liya
  • Wang, You-Gan
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    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.

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    Article provided by Elsevier in its journal Computational Statistics & Data Analysis.

    Volume (Year): 56 (2012)
    Issue (Month): 8 ()
    Pages: 2526-2538

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    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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    1. Hansen, Lars Peter, 1982. "Large Sample Properties of Generalized Method of Moments Estimators," Econometrica, Econometric Society, vol. 50(4), pages 1029-54, July.
    2. Sin-Ho Jung, 2003. "Rank-based regression with repeated measurements data," Biometrika, Biometrika Trust, vol. 90(3), pages 732-740, September.
    3. Koenker, Roger W & Bassett, Gilbert, Jr, 1978. "Regression Quantiles," Econometrica, Econometric Society, vol. 46(1), pages 33-50, January.
    4. Koenker,Roger, 2005. "Quantile Regression," Cambridge Books, Cambridge University Press, number 9780521608275, November.
    5. Wang, You-Gan & Shao, Quanxi & Zhu, Min, 2009. "Quantile regression without the curse of unsmoothness," Computational Statistics & Data Analysis, Elsevier, vol. 53(10), pages 3696-3705, August.
    6. Vicente Núñez-Antón & Juan Rodríguez-Póo & Philippe Vieu, 1999. "Longitudinal data with nonstationary errors: a nonparametric three-stage approach," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 8(1), pages 201-231, June.
    7. Koenker, Roger, 2004. "Quantile regression for longitudinal data," Journal of Multivariate Analysis, Elsevier, vol. 91(1), pages 74-89, October.
    8. 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.
    9. Bilias, Yannis & Chen, Songnian & Ying, Zhiliang, 2000. "Simple resampling methods for censored regression quantiles," Journal of Econometrics, Elsevier, vol. 99(2), pages 373-386, December.
    10. 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.
    11. Guosheng Yin & Jianwen Cai, 2005. "Quantile Regression Models with Multivariate Failure Time Data," Biometrics, The International Biometric Society, vol. 61(1), pages 151-161, 03.
    12. Julie A. Stoner, 2002. "Analysis of clustered data: A combined estimating equations approach," Biometrika, Biometrika Trust, vol. 89(3), pages 567-578, August.
    13. Buchinsky, Moshe, 1995. "Estimating the asymptotic covariance matrix for quantile regression models a Monte Carlo study," Journal of Econometrics, Elsevier, vol. 68(2), pages 303-338, August.
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