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Variable selection in robust regression models for longitudinal data

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  • Fan, Yali
  • Qin, Guoyou
  • Zhu, Zhongyi

Abstract

In this article, we consider variable selection in robust regression models for longitudinal data. We propose a penalized robust estimating equation to estimate the regression parameters and to select the important covariate variables simultaneously. Under some regularity conditions, we show the oracle properties of the proposed robust variable selection methods. A simulation study shows the robustness of the proposed methods against outliers. Moreover, it is found by the simulation study that incorporating the correlation structure into the procedure of variable selection will lead to better performance than ignoring the correlation structure for longitudinal data. In the end, the proposed methods are illustrated in the analysis of a real data set.

Suggested Citation

  • Fan, Yali & Qin, Guoyou & Zhu, Zhongyi, 2012. "Variable selection in robust regression models for longitudinal data," Journal of Multivariate Analysis, Elsevier, vol. 109(C), pages 156-167.
    • Handle: RePEc:eee:jmvana:v:109:y:2012:i:c:p:156-167
    DOI: 10.1016/j.jmva.2012.03.007
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    References listed on IDEAS

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    Citations

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    Cited by:

    1. Wang, Kangning & Li, Shaomin & Sun, Xiaofei & Lin, Lu, 2019. "Modal regression statistical inference for longitudinal data semivarying coefficient models: Generalized estimating equations, empirical likelihood and variable selection," Computational Statistics & Data Analysis, Elsevier, vol. 133(C), pages 257-276.
    2. Jia Chen & Jiti Gao, 2014. "Semiparametric Model Selection in Panel Data Models with Deterministic Trends and Cross-Sectional Dependence," Monash Econometrics and Business Statistics Working Papers 15/14, Monash University, Department of Econometrics and Business Statistics.
    3. Chaohui Guo & Hu Yang & Jing Lv, 2018. "Two step estimations for a single-index varying-coefficient model with longitudinal data," Statistical Papers, Springer, vol. 59(3), pages 957-983, September.
    4. Guney, Yesim & Arslan, Olcay & Yavuz, Fulya Gokalp, 2022. "Robust estimation in multivariate heteroscedastic regression models with autoregressive covariance structures using EM algorithm," Journal of Multivariate Analysis, Elsevier, vol. 191(C).
    5. Kangning Wang & Mengjie Hao & Xiaofei Sun, 2021. "Robust and efficient estimating equations for longitudinal data partial linear models and its applications," Statistical Papers, Springer, vol. 62(5), pages 2147-2168, October.
    6. 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.
    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. 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.
    9. 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.
    10. 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.

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