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GMM in linear regression for longitudinal data with multiple covariates measured with error

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  • Zhiguo Xiao
  • Jun Shao
  • Mari Palta

Abstract

Griliches and Hausman 5 and Wansbeek 11 proposed using the generalized method of moments (GMM) to obtain consistent estimators in linear regression models for longitudinal data with measurement error in one covariate, without requiring additional validation or replicate data. For usefulness of this methodology, we must extend it to the more realistic situation where more than one covariate are measured with error. Such an extension is not straightforward, since measurement errors across different covariates may be correlated. By a careful construction of the measurement error correlation structure, we are able to extend Wansbeek's GMM and show that the extended Griliches and Hausman's GMM is equivalent to the extended Wansbeek's GMM. For illustration, we apply the extended GMM to data from two medical studies, and compare it with the naive method and the method assuming only one covariate having measurement error.

Suggested Citation

  • Zhiguo Xiao & Jun Shao & Mari Palta, 2010. "GMM in linear regression for longitudinal data with multiple covariates measured with error," Journal of Applied Statistics, Taylor & Francis Journals, vol. 37(5), pages 791-805.
    • Handle: RePEc:taf:japsta:v:37:y:2010:i:5:p:791-805
    DOI: 10.1080/02664760902890005
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    References listed on IDEAS

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    1. Wansbeek, Tom, 2001. "GMM estimation in panel data models with measurement error," Journal of Econometrics, Elsevier, vol. 104(2), pages 259-268, September.
    2. Bound, John & Brown, Charles & Mathiowetz, Nancy, 2001. "Measurement error in survey data," Handbook of Econometrics, in: J.J. Heckman & E.E. Leamer (ed.), Handbook of Econometrics, edition 1, volume 5, chapter 59, pages 3705-3843, Elsevier.
    3. Jeffrey M Wooldridge, 2010. "Econometric Analysis of Cross Section and Panel Data," MIT Press Books, The MIT Press, edition 2, volume 1, number 0262232588, April.
    4. Griliches, Zvi & Hausman, Jerry A., 1986. "Errors in variables in panel data," Journal of Econometrics, Elsevier, vol. 31(1), pages 93-118, February.
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    Cited by:

    1. Meijer, Erik & Spierdijk, Laura & Wansbeek, Tom, 2017. "Consistent estimation of linear panel data models with measurement error," Journal of Econometrics, Elsevier, vol. 200(2), pages 169-180.
    2. Jiachen Cai & Ning Zhang & Xin Zhou & Donna Spiegelman & Molin Wang, 2023. "Correcting for bias due to mismeasured exposure history in longitudinal studies with continuous outcomes," Biometrics, The International Biometric Society, vol. 79(4), pages 3739-3751, December.
    3. Bei Wang & Jeffrey R. Wilson, 2018. "Comparative GMM and GQL logistic regression models on hierarchical data," Journal of Applied Statistics, Taylor & Francis Journals, vol. 45(3), pages 409-425, February.

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