DOI QR코드

DOI QR Code

Bootstrap Estimation for GEE Models

일반화추정방정식(GEE)에 대한 부스트랩의 적용

Park, Chong-Sun;Jeon, Yong-Moon
박종선;전용문

  • Received : 20101000
  • Accepted : 20101200
  • Published : 2011.02.28

Abstract

Bootstrap is a resampling technique to find an estimate of parameters or to evaluate the estimate. This technique has been used in estimating parameters in linear model(LM) and generalized linear model(GLM). In this paper, we explore the possibility of applying Bootstrapping Residuals, Pairs, and an Estimating Equation that are most widely used in LM and GLM to the generalized estimating equation(GEE) algorithm for modelling repeatedly measured regression data sets. We compared three bootstrapping methods with coefficient and standard error estimates of GEE models from one simulated and one real data set. Overall, the estimates obtained from bootstrap methods are quite comparable, except that estimates from bootstrapping pairs are somewhat different from others. We conjecture that the strange behavior of estimates from bootstrapping pairs comes from the inconsistency of those estimates. However, we need a more thorough simulation study to generalize it since those results are coming from only two small data sets.

Keywords

Regression model;generalized estimating equation;bootstrap method

References

  1. Chatterjee, S. and Bose, A. (2005). Generalized Bootstrapping for estimating equation, The Annals of Statistics, 33, 414–436.
  2. Efron, B. (1979). Bootstrap methods: Another look at the jackknife, The Annals of Statistics, 7, 1–26.
  3. Freedman, D. (1981). Bootstraping regression model, The Annals of Statistics, 9, 1218–1228.
  4. Freedman, D. and Peters, S. (1984). Bootstraping a regression equation, Journal of the American Statistical Association, 79, 97-106. https://doi.org/10.2307/2288341
  5. Friedl, H. and Stadlober, E. (1997). Resampling methods in generalized linear models useful in environmetrics, Environmetrics, 8, 441–457.
  6. Hardin, J. W. and Hilbe, J. M. (2002). Generalized Estimating Equations, Chapman & Hall, New York.
  7. Hu, F. and Kalbfleisch, J. (2000). The estimating function bootstrap (with discussion), The Canadian Journal of Statistics, 28, 449-499. https://doi.org/10.2307/3315958
  8. Hu, F. and Zidek, J. (1995). A bootstrap based on the estimating equations of the linear model, Biometrika, 82, 263-275. https://doi.org/10.1093/biomet/82.2.263
  9. Lele, S. R. (1991). Resampling using estimating equation, In Estimating Functions (V.P. Godambe, ed.), 295–304, Oxford University Press.
  10. Liang, K. and Zeger, S. (1986). Longitudinal data analysis using generalized linear models, Biometrika, 73, 13-22. https://doi.org/10.1093/biomet/73.1.13
  11. McCullagh, P. (1983). Quasi-likelihood function, The Annals of Statistics, 11, 59-67. https://doi.org/10.1214/aos/1176346056
  12. McCullagh, P. and Nelder (1989). Generalized Linear Models 2nd edition, Chapman & Hall, New York.
  13. Moulton, L. and Zeger, S. (1989). Analyzing repeated measures on generalized linear models via the bootstrap, Biometrics, 45, 381–394.
  14. Moulton, L. and Zeger, S. (1991). Bootstrapping generalized linear models, Computational Statistics & Data Analysis, 11, 53-63. https://doi.org/10.1016/0167-9473(91)90052-4
  15. Simonoff, J. S. and Tsai, C. L. (1988). Jackknifing & bootstrapping quasi-likelihood estimators, Journal of Statistical Computation and Simulation, 30, 213-232. https://doi.org/10.1080/00949658808811098
  16. Ware, J., Dockery, D., Spiro, A., Speizer, F. and Ferris, B. (1984). Passive smoking, gas cooking and respiratory health of children living in six cities, Am. Rev. Respir. Dis., 129, 366-374.
  17. Wedderburn, R. (1974). Quasi-likelihood function, generalized linear models, and Gauss-Newton method. Biometrika, 61, 439-447.
  18. Wu, C. (1986). Jackknife, bootstrap and other resampling methods in regression analysis, The Annals of Statistics, 14, 1261–1295.