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Robust estimation in generalized semiparametric mixed models for longitudinal data

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  • Qin, Guoyou
  • Zhu, Zhongyi

Abstract

In this paper, we consider robust generalized estimating equations for the analysis of semiparametric generalized partial linear mixed models (GPLMMs) for longitudinal data. We approximate the non-parametric function in the GPLMM by a regression spline, and make use of bounded scores and leverage-based weights in the estimating equation to achieve robustness against outliers and influential data points, respectively. Under some regularity conditions, the asymptotic properties of the robust estimators are investigated. To avoid the computational problems involving high-dimensional integrals in our estimators, we adopt a robust Monte Carlo Newton-Raphson (RMCNR) algorithm for fitting GPLMMs. Small simulations are carried out to study the behavior of the robust estimates in the presence of outliers, and these estimates are also compared to their corresponding non-robust estimates. The proposed robust method is illustrated in the analysis of two real data sets.

Suggested Citation

  • Qin, Guoyou & Zhu, Zhongyi, 2007. "Robust estimation in generalized semiparametric mixed models for longitudinal data," Journal of Multivariate Analysis, Elsevier, vol. 98(8), pages 1658-1683, September.
    • Handle: RePEc:eee:jmvana:v:98:y:2007:i:8:p:1658-1683
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    References listed on IDEAS

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    1. You-Gan Wang & Xu Lin & Min Zhu, 2005. "Robust Estimating Functions and Bias Correction for Longitudinal Data Analysis," Biometrics, The International Biometric Society, vol. 61(3), pages 684-691, September.
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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. Xueying Zheng & Wing Fung & Zhongyi Zhu, 2013. "Robust estimation in joint mean–covariance regression model for longitudinal data," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 65(4), pages 617-638, August.
    3. M. Taavoni & M. Arashi, 2021. "Kernel estimation in semiparametric mixed effect longitudinal modeling," Statistical Papers, Springer, vol. 62(3), pages 1095-1116, June.
    4. Boente, Graciela & Rodriguez, Daniela, 2010. "Robust inference in generalized partially linear models," Computational Statistics & Data Analysis, Elsevier, vol. 54(12), pages 2942-2966, December.
    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. Tang, Nian-Sheng & Duan, Xing-De, 2012. "A semiparametric Bayesian approach to generalized partial linear mixed models for longitudinal data," Computational Statistics & Data Analysis, Elsevier, vol. 56(12), pages 4348-4365.
    7. Huiming Lin & Bo Fu & Guoyou Qin & Zhongyi Zhu, 2017. "Doubly robust estimation of generalized partial linear models for longitudinal data with dropouts," Biometrics, The International Biometric Society, vol. 73(4), pages 1132-1139, December.
    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. Qin, Guoyou & Bai, Yang & Zhu, Zhongyi, 2012. "Robust empirical likelihood inference for generalized partial linear models with longitudinal data," Journal of Multivariate Analysis, Elsevier, vol. 105(1), pages 32-44.
    10. Chen, Xue-Dong & Tang, Nian-Sheng, 2010. "Bayesian analysis of semiparametric reproductive dispersion mixed-effects models," Computational Statistics & Data Analysis, Elsevier, vol. 54(9), pages 2145-2158, September.
    11. Guo You Qin & Zhong Yi Zhu, 2009. "Robustified Maximum Likelihood Estimation in Generalized Partial Linear Mixed Model for Longitudinal Data," Biometrics, The International Biometric Society, vol. 65(1), pages 52-59, March.
    12. 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.
    13. Mozhgan Taavoni & Mohammad Arashi & Samuel Manda, 2023. "Multicollinearity and Linear Predictor Link Function Problems in Regression Modelling of Longitudinal Data," Mathematics, MDPI, vol. 11(3), pages 1-9, January.

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