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A functional generalized method of moments approach for longitudinal studies with missing responses and covariate measurement error

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  • Grace Y. Yi
  • Yanyuan Ma
  • Raymond J. Carroll

Abstract

Covariate measurement error and missing responses are typical features in longitudinal data analysis. There has been extensive research on either covariate measurement error or missing responses, but relatively little work has been done to address both simultaneously. In this paper, we propose a simple method for the marginal analysis of longitudinal data with time-varying covariates, some of which are measured with error, while the response is subject to missingness. Our method has a number of appealing properties: assumptions on the model are minimal, with none needed about the distribution of the mismeasured covariate; implementation is straightforward and its applicability is broad. We provide both theoretical justification and numerical results. Copyright 2012, Oxford University Press.

Suggested Citation

  • 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.
    • Handle: RePEc:oup:biomet:v:99:y:2012:i:1:p:151-165
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    File URL: http://hdl.handle.net/10.1093/biomet/asr076
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    Cited by:

    1. Glen McGee & Marianthi‐Anna Kioumourtzoglou & Marc G. Weisskopf & Sebastien Haneuse & Brent A. Coull, 2020. "On the interplay between exposure misclassification and informative cluster size," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 69(5), pages 1209-1226, November.
    2. Jun Zhang & Zhenghui Feng & Peirong Xu & Hua Liang, 2017. "Generalized varying coefficient partially linear measurement errors models," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 69(1), pages 97-120, February.
    3. Yih-Huei Huang & Chi-Chung Wen & Yu-Hua Hsu, 2015. "The Extensively Corrected Score for Measurement Error Models," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 42(4), pages 911-924, December.
    4. J. R. Lockwood & Daniel F. McCaffrey, 2019. "Impact Evaluation Using Analysis of Covariance With Error-Prone Covariates That Violate Surrogacy," Evaluation Review, , vol. 43(6), pages 335-369, December.
    5. J. R. Lockwood & D. McCaffrey, 2020. "Using hidden information and performance level boundaries to study student–teacher assignments: implications for estimating teacher causal effects," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 183(4), pages 1333-1362, October.
    6. Grace Y. Yi & Yanyuan Ma & Donna Spiegelman & Raymond J. Carroll, 2015. "Functional and Structural Methods With Mixed Measurement Error and Misclassification in Covariates," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 110(510), pages 681-696, June.
    7. 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.
    8. Trang Quynh Nguyen & Elizabeth A. Stuart, 2020. "Propensity Score Analysis With Latent Covariates: Measurement Error Bias Correction Using the Covariate’s Posterior Mean, aka the Inclusive Factor Score," Journal of Educational and Behavioral Statistics, , vol. 45(5), pages 598-636, October.
    9. 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.
    10. 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.
    11. 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.
    12. 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.
    13. Marie-Ann Sengewald & Steffi Pohl, 2019. "Compensation and Amplification of Attenuation Bias in Causal Effect Estimates," Psychometrika, Springer;The Psychometric Society, vol. 84(2), pages 589-610, June.

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