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Robust estimation in generalized semiparametric mixed models for longitudinal data

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  • Qin, Guoyou
  • Zhu, Zhongyi
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    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.

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    Bibliographic Info

    Article provided by Elsevier in its journal Journal of Multivariate Analysis.

    Volume (Year): 98 (2007)
    Issue (Month): 8 (September)
    Pages: 1658-1683

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    Handle: RePEc:eee:jmvana:v:98:y:2007:i:8:p:1658-1683

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    Related research

    Keywords: B-spline Generalized linear models Longitudinal data Metropolis algorithm Mixed model Newton-Raphson algorithm Partial linear models Robustness;

    References

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    1. 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.
    2. He, Xuming & Fung, Wing K. & Zhu, Zhongyi, 2005. "Robust Estimation in Generalized Partial Linear Models for Clustered Data," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 1176-1184, December.
    3. Lin X. & Carroll R. J., 2001. "Semiparametric Regression for Clustered Data Using Generalized Estimating Equations," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 1045-1056, September.
    4. Sinha S.K., 2004. "Robust Analysis of Generalized Linear Mixed Models," Journal of the American Statistical Association, American Statistical Association, vol. 99, pages 451-460, January.
    5. Xuming He, 2002. "Estimation in a semiparametric model for longitudinal data with unspecified dependence structure," Biometrika, Biometrika Trust, vol. 89(3), pages 579-590, August.
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    Cited by:
    1. Boente, Graciela & Rodriguez, Daniela, 2010. "Robust inference in generalized partially linear models," Computational Statistics & Data Analysis, Elsevier, vol. 54(12), pages 2942-2966, December.
    2. 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.
    3. 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, vol. 65(4), pages 617-638, August.
    4. 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.

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