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Simultaneous mean and covariance estimation of partially linear models for longitudinal data with missing responses and covariate measurement error

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  • Qin, Guoyou
  • Zhang, Jiajia
  • Zhu, Zhongyi

Abstract

Missing responses and covariate measurement error are very commonly seen in practice. New estimating equations are developed to simultaneously estimate the mean and covariance under a partially linear model for longitudinal data with missing responses and covariate measurement error. Specifically, a novel approach is proposed to handle measurement error by using independent replicate measurements. Compared with existing methods, the proposed method requires fewer assumptions. For example, it does not require to specify the distribution of the mismeasured covariate or the measurement error, and does not need a parametric model to estimate the probability of being observed or to impute the missing responses. Additionally, the proposed estimating equations are easy to implement in most popular statistical softwares by applying existing algorithms for standard generalized estimating equations. The asymptotic properties of the proposed estimators are established under regularity conditions, and simulation studies demonstrate desired properties. Finally, the proposed method is applied to data from the Lifestyle Education for Activity and Nutrition (LEAN) study. This data analysis confirms the effectiveness of the intervention in producing weight loss at month nine.

Suggested Citation

  • 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.
  • Handle: RePEc:eee:csdana:v:96:y:2016:i:c:p:24-39
    DOI: 10.1016/j.csda.2015.11.001
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    Cited by:

    1. 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.
    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. 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).
    5. 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.

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