IDEAS home Printed from https://ideas.repec.org/a/eee/jmvana/v98y2007i8p1658-1683.html
   My bibliography  Save this article

Robust estimation in generalized semiparametric mixed models for longitudinal data

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0047-259X(07)00003-6
    Download Restriction: Full text for ScienceDirect subscribers only
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    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.
    2. 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.
    3. 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.
    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. 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.
    6. 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.
    7. John S. Preisser & Bahjat F. Qaqish, 1999. "Robust Regression for Clustered Data with Application to Binary Responses," Biometrics, The International Biometric Society, vol. 55(2), pages 574-579, June.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    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. 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.
    5. 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.
    6. 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.
    7. Boente, Graciela & Rodriguez, Daniela, 2010. "Robust inference in generalized partially linear models," Computational Statistics & Data Analysis, Elsevier, vol. 54(12), pages 2942-2966, December.
    8. 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.
    9. 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.
    10. 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.
    11. 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.
    12. 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.
    13. 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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. 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.
    2. Qin, Guo You & Zhu, Zhong Yi & Fung, Wing K., 2008. "Robust estimating equations and bias correction of correlation parameters for longitudinal data," Computational Statistics & Data Analysis, Elsevier, vol. 52(10), pages 4745-4753, June.
    3. Zhang, Yuexia & Qin, Guoyou & Zhu, Zhongyi & Zhang, Jiajia, 2018. "Robust estimation in linear regression models for longitudinal data with covariate measurement errors and outliers," Journal of Multivariate Analysis, Elsevier, vol. 168(C), pages 261-275.
    4. Liu, Anna & Qin, Li & Staudenmayer, John, 2010. "M-type smoothing spline ANOVA for correlated data," Journal of Multivariate Analysis, Elsevier, vol. 101(10), pages 2282-2296, November.
    5. Qin, Guoyou & Bai, Yang & Zhu, Zhongyi, 2009. "Robust empirical likelihood inference for longitudinal data," Statistics & Probability Letters, Elsevier, vol. 79(20), pages 2101-2108, October.
    6. Kalyan Das & Angshuman Sarkar, 2014. "Robust inference for generalized partially linear mixed models that account for censored responses and missing covariates -- an application to Arctic data analysis," Journal of Applied Statistics, Taylor & Francis Journals, vol. 41(11), pages 2418-2436, November.
    7. 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.
    8. J. E. Mills & C. A. Field & D. J. Dupuis, 2002. "Marginally Specified Generalized Linear Mixed Models: A Robust Approach," Biometrics, The International Biometric Society, vol. 58(4), pages 727-734, December.
    9. 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.
    10. 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.
    11. Guoyou Qin & Zhongyi Zhu & Wing Fung, 2012. "Robust estimation of the generalised partial linear model with missing covariates," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 24(2), pages 517-530.
    12. Li, Gaorong & Zhu, Lixing & Xue, Liugen & Feng, Sanying, 2010. "Empirical likelihood inference in partially linear single-index models for longitudinal data," Journal of Multivariate Analysis, Elsevier, vol. 101(3), pages 718-732, March.
    13. Zou, Yubo & Zhang, Jiajia & Qin, Guoyou, 2011. "A semiparametric accelerated failure time partial linear model and its application to breast cancer," Computational Statistics & Data Analysis, Elsevier, vol. 55(3), pages 1479-1487, March.
    14. 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.
    15. Ma, Shujie & Liang, Hua & Tsai, Chih-Ling, 2014. "Partially linear single index models for repeated measurements," Journal of Multivariate Analysis, Elsevier, vol. 130(C), pages 354-375.
    16. Rui Li & Chenlei Leng & Jinhong You, 2017. "A Semiparametric Regression Model for Longitudinal Data with Non-stationary Errors," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 44(4), pages 932-950, December.
    17. Du, Jiang & Sun, Zhimeng & Xie, Tianfa, 2013. "M-estimation for the partially linear regression model under monotonic constraints," Statistics & Probability Letters, Elsevier, vol. 83(5), pages 1353-1363.
    18. Tian, Ruiqin & Xue, Liugen & Xu, Dengke, 2016. "Automatic variable selection for varying coefficient models with longitudinal data," Statistics & Probability Letters, Elsevier, vol. 119(C), pages 84-90.
    19. Tian, Ruiqin & Xue, Liugen & Liu, Chunling, 2014. "Penalized quadratic inference functions for semiparametric varying coefficient partially linear models with longitudinal data," Journal of Multivariate Analysis, Elsevier, vol. 132(C), pages 94-110.
    20. Li, Shaomin & Wang, Kangning & Ren, Yanyan, 2018. "Robust estimation and empirical likelihood inference with exponential squared loss for panel data models," Economics Letters, Elsevier, vol. 164(C), pages 19-23.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:jmvana:v:98:y:2007:i:8:p:1658-1683. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/wps/find/journaldescription.cws_home/622892/description#description .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.