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일반화추정방정식(GEE)에 대한 부스트랩의 적용

Bootstrap Estimation for GEE Models

  • 투고 : 20101000
  • 심사 : 20101200
  • 발행 : 2011.02.28

초록

본 논문에서는 일반화추정방정식(GEE)모형에 대한 부스트랩 방법의 적용에 대하여 살펴본다. 다양한 부스트랩 방법들 중 GEE모형에 적용이 가능한 잔차, 쌍 및 점수함수 부스트랩 방법을 가상 및 실제 자료들에 적용한 결과 회귀계수들에 대한 추정치와 표준오차가 점근값들과 차이를 보이는 것으로 나타났다. 따라서 표본수가 크지 않은 경우 부스트랩 방법을 통하여 GEE모형에서의 회귀계수에 대한 추정치화 표준편차를 구하는 것이 효과적임을 알 수 있다.

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.

키워드

참고문헌

  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.