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Quantile regression for nonlinear mixed effects models: a likelihood based perspective

Author

Listed:
  • Christian E. Galarza

    (Escuela Superior Politécnica del Litoral, ESPOL
    Universidade Estadual de Campinas)

  • Luis M. Castro

    (Pontificia Universidad Católica de Chile)

  • Francisco Louzada

    (Universidade de São Paulo)

  • Victor H. Lachos

    (University of Connecticut)

Abstract

Longitudinal data are frequently analyzed using normal mixed effects models. Moreover, the traditional estimation methods are based on mean regression, which leads to non-robust parameter estimation under non-normal error distribution. However, at least in principle, quantile regression (QR) is more robust in the presence of outliers/influential observations and misspecification of the error distributions when compared to the conventional mean regression approach. In this context, this paper develops a likelihood-based approach for estimating QR models with correlated continuous longitudinal data using the asymmetric Laplace distribution. Our approach relies on the stochastic approximation of the EM algorithm (SAEM algorithm), obtaining maximum likelihood estimates of the fixed effects and variance components in the case of nonlinear mixed effects (NLME) models. We evaluate the finite sample performance of the SAEM algorithm and asymptotic properties of the ML estimates through simulation experiments. Moreover, two real life datasets are used to illustrate our proposed method using the $$\texttt {qrNLMM}$$qrNLMM package from $$\texttt {R}$$R.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:stpapr:v:61:y:2020:i:3:d:10.1007_s00362-018-0988-y
    DOI: 10.1007/s00362-018-0988-y
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    References listed on IDEAS

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    1. 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.
    2. Galvao Jr., Antonio F., 2011. "Quantile regression for dynamic panel data with fixed effects," Journal of Econometrics, Elsevier, vol. 164(1), pages 142-157, September.
    3. Koenker, Roger, 2004. "Quantile regression for longitudinal data," Journal of Multivariate Analysis, Elsevier, vol. 91(1), pages 74-89, October.
    4. J. G. Booth & J. P. Hobert, 1999. "Maximizing generalized linear mixed model likelihoods with an automated Monte Carlo EM algorithm," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 61(1), pages 265-285.
    5. Lachos, Victor H. & Castro, Luis M. & Dey, Dipak K., 2013. "Bayesian inference in nonlinear mixed-effects models using normal independent distributions," Computational Statistics & Data Analysis, Elsevier, vol. 64(C), pages 237-252.
    6. Mu, Yunming & He, Xuming, 2007. "Power Transformation Toward a Linear Regression Quantile," Journal of the American Statistical Association, American Statistical Association, vol. 102, pages 269-279, March.
    7. Alan S. Perelson & Paulina Essunger & Yunzhen Cao & Mika Vesanen & Arlene Hurley & Kalle Saksela & Martin Markowitz & David D. Ho, 1997. "Decay characteristics of HIV-1-infected compartments during combination therapy," Nature, Nature, vol. 387(6629), pages 188-191, May.
    8. Tomasz Kozubowski & Saralees Nadarajah, 2010. "Multitude of Laplace distributions," Statistical Papers, Springer, vol. 51(1), pages 127-148, January.
    9. Ying Yuan & Guosheng Yin, 2010. "Bayesian Quantile Regression for Longitudinal Studies with Nonignorable Missing Data," Biometrics, The International Biometric Society, vol. 66(1), pages 105-114, 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. A. Aghamohammadi & S. Mohammadi, 2017. "Bayesian analysis of penalized quantile regression for longitudinal data," Statistical Papers, Springer, vol. 58(4), pages 1035-1053, December.
    12. Jing Wang, 2012. "Bayesian quantile regression for parametric nonlinear mixed effects models," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 21(3), pages 279-295, August.
    13. Ole E. Barndorff‐Nielsen & Neil Shephard, 2001. "Non‐Gaussian Ornstein–Uhlenbeck‐based models and some of their uses in financial economics," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 63(2), pages 167-241.
    14. Yu, Keming & Moyeed, Rana A., 2001. "Bayesian quantile regression," Statistics & Probability Letters, Elsevier, vol. 54(4), pages 437-447, October.
    15. Yangxin Huang & Getachew Dagne, 2011. "A Bayesian Approach to Joint Mixed-Effects Models with a Skew-Normal Distribution and Measurement Errors in Covariates," Biometrics, The International Biometric Society, vol. 67(1), pages 260-269, March.
    16. Kuhn, E. & Lavielle, M., 2005. "Maximum likelihood estimation in nonlinear mixed effects models," Computational Statistics & Data Analysis, Elsevier, vol. 49(4), pages 1020-1038, June.
    17. Wu L., 2002. "A Joint Model for Nonlinear Mixed-Effects Models With Censoring and Covariates Measured With Error, With Application to AIDS Studies," Journal of the American Statistical Association, American Statistical Association, vol. 97, pages 955-964, December.
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