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The cluster bootstrap consistency in generalized estimating equations

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  • Cheng, Guang
  • Yu, Zhuqing
  • Huang, Jianhua Z.

Abstract

The cluster bootstrap resamples clusters or subjects instead of individual observations in order to preserve the dependence within each cluster or subject. In this paper, we provide a theoretical justification of using the cluster bootstrap for the inferences of the generalized estimating equations (GEE) for clustered/longitudinal data. Under the general exchangeable bootstrap weights, we show that the cluster bootstrap yields a consistent approximation of the distribution of the regression estimate, and a consistent approximation of the confidence sets. We also show that a computationally more efficient one-step version of the cluster bootstrap provides asymptotically equivalent inference.

Suggested Citation

  • Cheng, Guang & Yu, Zhuqing & Huang, Jianhua Z., 2013. "The cluster bootstrap consistency in generalized estimating equations," Journal of Multivariate Analysis, Elsevier, vol. 115(C), pages 33-47.
    • Handle: RePEc:eee:jmvana:v:115:y:2013:i:c:p:33-47
    DOI: 10.1016/j.jmva.2012.09.003
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    References listed on IDEAS

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    1. A. Colin Cameron & Jonah B. Gelbach & Douglas L. Miller, 2008. "Bootstrap-Based Improvements for Inference with Clustered Errors," The Review of Economics and Statistics, MIT Press, vol. 90(3), pages 414-427, August.
    2. Lloyd A. Mancl & Timothy A. DeRouen, 2001. "A Covariance Estimator for GEE with Improved Small‐Sample Properties," Biometrics, The International Biometric Society, vol. 57(1), pages 126-134, March.
    3. Kauermann G. & Carroll R.J., 2001. "A Note on the Efficiency of Sandwich Covariance Matrix Estimation," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 1387-1396, December.
    4. You-Gan Wang, 2003. "Working correlation structure misspecification, estimation and covariate design: Implications for generalised estimating equations performance," Biometrika, Biometrika Trust, vol. 90(1), pages 29-41, March.
    5. C. A. Field & A. H. Welsh, 2007. "Bootstrapping clustered data," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 69(3), pages 369-390, June.
    6. You-Gan Wang & Vincent J. Carey, 2004. "Unbiased Estimating Equations From Working Correlation Models for Irregularly Timed Repeated Measures," Journal of the American Statistical Association, American Statistical Association, vol. 99, pages 845-853, January.
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    Cited by:

    1. Victor Chernozhukov & Iván Fernández-Val & Blaise Melly & Kaspar Wüthrich, 2020. "Generic Inference on Quantile and Quantile Effect Functions for Discrete Outcomes," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 115(529), pages 123-137, January.
    2. Hailemichael M. Worku & Mark Rooij, 2018. "A Multivariate Logistic Distance Model for the Analysis of Multiple Binary Responses," Journal of Classification, Springer;The Classification Society, vol. 35(1), pages 124-146, April.
    3. Sant’Anna, Pedro H.C. & Zhao, Jun, 2020. "Doubly robust difference-in-differences estimators," Journal of Econometrics, Elsevier, vol. 219(1), pages 101-122.
    4. Brantly Callaway & Pedro H. C. Sant'Anna, 2018. "Difference-in-Differences with Multiple Time Periods and an Application on the Minimum Wage and Employment," DETU Working Papers 1804, Department of Economics, Temple University.
    5. Guang Cheng, 2013. "How Many Iterations are Sufficient for Efficient Semiparametric Estimation?," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 40(3), pages 592-618, September.
    6. Callaway, Brantly & Sant’Anna, Pedro H.C., 2021. "Difference-in-Differences with multiple time periods," Journal of Econometrics, Elsevier, vol. 225(2), pages 200-230.
    7. Hudecová, Šárka & Pešta, Michal, 2013. "Modeling dependencies in claims reserving with GEE," Insurance: Mathematics and Economics, Elsevier, vol. 53(3), pages 786-794.
    8. Anthony M. Evans & Joachim I. Krueger, 2014. "Outcomes and expectations in dilemmas of trust," Judgment and Decision Making, Society for Judgment and Decision Making, vol. 9(2), pages 90-103, March.
    9. Martin Spiess & Pascal Jordan & Mike Wendt, 2019. "Simplified Estimation and Testing in Unbalanced Repeated Measures Designs," Psychometrika, Springer;The Psychometric Society, vol. 84(1), pages 212-235, March.
    10. repec:cup:judgdm:v:9:y:2014:i:2:p:90-103 is not listed on IDEAS
    11. Mark Rooij, 2018. "Transitional modeling of experimental longitudinal data with missing values," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 12(1), pages 107-130, March.
    12. He, Hongwei & Hu, Yansong, 2021. "The dynamic impacts of shared leadership and the transactive memory system on team performance: A longitudinal study," Journal of Business Research, Elsevier, vol. 130(C), pages 14-26.

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