IDEAS home Printed from https://ideas.repec.org/a/eee/csdana/v121y2018icp104-112.html
   My bibliography  Save this article

Analysis of longitudinal data with covariate measurement error and missing responses: An improved unbiased estimating equation

Author

Listed:
  • Lin, Huiming
  • Qin, Guoyou
  • Zhang, Jiajia
  • Zhu, Zhongyi

Abstract

Because of the data collection process, measurement error and missing responses are common in longitudinal data, and correctly addressing these scenarios becomes one of main challenges in longitudinal data analysis. First, an unbiased estimating equation is proposed to improve the efficiency of parameter estimations for the marginal mean model for longitudinal data with covariate measurement error. The proposed unbiased estimating equation is asymptotically more efficient than the method in Qin et al. (2016a). Second, the proposed method can be extended to handle more complicated scenarios. Specifically, robust estimation for partially linear models with missing responses and covariate measurement error is considered. The proposed robust estimation does not require specifying the distribution of the covariate or the measurement error and is computationally easy to implement. Simulation studies are conducted to evaluate the improvement of the proposed method over existing methods (Qin et al., 2016b), and a sketch of the proof of its asymptotic property is provided. Finally, the proposed method is applied to the data from the Lifestyle Education for Activity and Nutrition (LEAN) study.

Suggested Citation

  • Lin, Huiming & Qin, Guoyou & Zhang, Jiajia & Zhu, Zhongyi, 2018. "Analysis of longitudinal data with covariate measurement error and missing responses: An improved unbiased estimating equation," Computational Statistics & Data Analysis, Elsevier, vol. 121(C), pages 104-112.
    • Handle: RePEc:eee:csdana:v:121:y:2018:i:c:p:104-112
    DOI: 10.1016/j.csda.2017.11.010
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167947317302554
    Download Restriction: Full text for ScienceDirect subscribers only.
    File URL: https://libkey.io/10.1016/j.csda.2017.11.010?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    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. 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.
    2. Qin, Guoyou & Zhang, Jiajia & Zhu, Zhongyi, 2016. "Simultaneous mean and covariance estimation of partially linear models for longitudinal data with missing responses and covariate measurement error," Computational Statistics & Data Analysis, Elsevier, vol. 96(C), pages 24-39.
    3. He, Xuming & Shi, Peide, 1996. "Bivariate Tensor-Product B-Splines in a Partly Linear Model," Journal of Multivariate Analysis, Elsevier, vol. 58(2), pages 162-181, August.
    4. Grace Y. Yi & Yanyuan Ma & Raymond J. Carroll, 2012. "A functional generalized method of moments approach for longitudinal studies with missing responses and covariate measurement error," Biometrika, Biometrika Trust, vol. 99(1), pages 151-165.
    5. D. Rummel & T. Augustin & H. Küchenhoff, 2010. "Correction for Covariate Measurement Error in Nonparametric Longitudinal Regression," Biometrics, The International Biometric Society, vol. 66(4), pages 1209-1219, December.
    6. Xihong Lin & Raymond J. Carroll, 2006. "Semiparametric estimation in general repeated measures problems," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 68(1), pages 69-88, February.
    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. Zhang, Yuexia & Qin, Guoyou & Zhu, Zhongyi & Zhang, Jiajia, 2022. "Empirical likelihood inference for longitudinal data with covariate measurement errors: An application to the LEAN study," Computational Statistics & Data Analysis, Elsevier, vol. 175(C).
    2. 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.

    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. Qin, Guoyou & Zhang, Jiajia & Zhu, Zhongyi, 2016. "Simultaneous mean and covariance estimation of partially linear models for longitudinal data with missing responses and covariate measurement error," Computational Statistics & Data Analysis, Elsevier, vol. 96(C), pages 24-39.
    2. 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.
    3. 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.
    4. 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.
    5. 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.
    6. 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.
    7. 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.
    8. Mengli Zhang & Yang Bai, 2021. "On the use of repeated measurement errors in linear regression models," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 84(5), pages 779-803, July.
    9. Ma, Shujie & Linton, Oliver & Gao, Jiti, 2021. "Estimation and inference in semiparametric quantile factor models," Journal of Econometrics, Elsevier, vol. 222(1), pages 295-323.
    10. Horowitz, Joel L. & Lee, Sokbae, 2005. "Nonparametric Estimation of an Additive Quantile Regression Model," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 1238-1249, December.
    11. Jiguo Cao & Liangliang Wang & Zhongwen Huang & Junyi Gai & Rongling Wu, 2017. "Functional Mapping of Multiple Dynamic Traits," Journal of Agricultural, Biological and Environmental Statistics, Springer;The International Biometric Society;American Statistical Association, vol. 22(1), pages 60-75, March.
    12. Aurore Delaigle & Peter Hall, 2016. "Methodology for non-parametric deconvolution when the error distribution is unknown," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 78(1), pages 231-252, January.
    13. Kan K & Lee M, 2009. "Lose Weight for Money Only if Over-Weight: Marginal Integration for Semi-Linear Panel Models," Health, Econometrics and Data Group (HEDG) Working Papers 09/19, HEDG, c/o Department of Economics, University of York.
    14. Zhang, Junhua & Feng, Sanying & Li, Gaorong & Lian, Heng, 2011. "Empirical likelihood inference for partially linear panel data models with fixed effects," Economics Letters, Elsevier, vol. 113(2), pages 165-167.
    15. Shakhawat Hossain & Le An Lac, 2021. "Optimal shrinkage estimations in partially linear single-index models for binary longitudinal data," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 30(4), pages 811-835, December.
    16. Tang Qingguo, 2009. "Asymptotic normality of M-estimators in a semiparametric model with longitudinal data," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 69(1), pages 55-67, January.
    17. Brajendra C. Sutradhar & Vandna Jowaheer & R. Prabhakar Rao, 2016. "Semi-Parametric Models for Negative Binomial Panel Data," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 78(2), pages 269-303, August.
    18. He, Xuming & Liang, Hua, 1997. "Quantile regression estimates for a class of linear and partially linear errors-in-variables models," SFB 373 Discussion Papers 1997,103, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
    19. Yujing Shao & Lei Wang, 2022. "Generalized partial linear models with nonignorable dropouts," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 85(2), pages 223-252, February.
    20. Firouzeh Noghrehchi & Jakub Stoklosa & Spiridon Penev, 2020. "Multiple imputation and functional methods in the presence of measurement error and missingness in explanatory variables," Computational Statistics, Springer, vol. 35(3), pages 1291-1317, September.

    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:csdana:v:121:y:2018:i:c:p:104-112. 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/locate/csda .

    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.