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An efficient and robust variable selection method for longitudinal generalized linear models

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  • Lv, Jing
  • Yang, Hu
  • Guo, Chaohui

Abstract

This paper presents a new efficient and robust smooth-threshold generalized estimating equations for generalized linear models (GLMs) with longitudinal data. The proposed method is based on a bounded exponential score function and leverage-based weights to achieve robustness against outliers both in the response and the covariate domain. Our motivation for the new variable selection procedure is that it enables us to achieve better robustness and efficiency by introducing an additional tuning parameter γ which can be automatically selected using the observed data. Moreover, its performance is near optimal and superior to some recently developed variable selection methods. Under some regularity conditions, the resulting estimator possesses the consistency in variable selection and the oracle property in estimation. Finally, simulation studies and a detailed real data analysis are carried out to assess and illustrate the finite sample performance, which show that the proposed method works better than other existing methods, in particular, when many outliers are included.

Suggested Citation

  • Lv, Jing & Yang, Hu & Guo, Chaohui, 2015. "An efficient and robust variable selection method for longitudinal generalized linear models," Computational Statistics & Data Analysis, Elsevier, vol. 82(C), pages 74-88.
    • Handle: RePEc:eee:csdana:v:82:y:2015:i:c:p:74-88
    DOI: 10.1016/j.csda.2014.08.006
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    References listed on IDEAS

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    5. You‐Gan Wang & Xu Lin & Min Zhu, 2020. "Rejoinder to “Comment on ‘Wang et al. (2005), Robust estimating functions and bias correction for longitudinal data analysis’ by Nicola Lunardon and Giovanna Menardi”," Biometrics, The International Biometric Society, vol. 76(3), pages 1043-1044, September.
    6. Liya Fu & Zhuoran Yang & Fengjing Cai & You-Gan Wang, 2021. "Efficient and doubly-robust methods for variable selection and parameter estimation in longitudinal data analysis," Computational Statistics, Springer, vol. 36(2), pages 781-804, June.
    7. Kangning Wang & Lu Lin, 2019. "Robust and efficient estimator for simultaneous model structure identification and variable selection in generalized partial linear varying coefficient models with longitudinal data," Statistical Papers, Springer, vol. 60(5), pages 1649-1676, October.
    8. Kangning Wang & Wen Shan, 2021. "Copula and composite quantile regression-based estimating equations for longitudinal data," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 73(3), pages 441-455, June.
    9. Zhang, Yuexia & Qin, Guoyou & Zhu, Zhongyi & Xu, Wanghong, 2019. "A novel robust approach for analysis of longitudinal data," Computational Statistics & Data Analysis, Elsevier, vol. 138(C), pages 83-95.

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