응용통계연구 (The Korean Journal of Applied Statistics)

  • 제28권2호
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  • Pages.123-136
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  • 2015
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  • 1225-066X(pISSN)
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  • 2383-5818(eISSN)
한국통계학회 (The Korean Statistical Society)
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혼합효과모형의 리뷰

Review of Mixed-Effect Models

  • Lee, Youngjo (Department of Statistics, Seoul National University)
  • 투고 : 2015.04.16
  • 심사 : 2015.04.23
  • 발행 : 2015.04.30
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⟨ 이전 논문 다음 논문 ⟩

초록

관측 가능한 변수들 사이의 관계를 묘사한 갈릴레오의 물리학 법칙 발견 이후, 과학은 큰 성과를 거두며 발전해왔다. 그러나, 관측할 수 없는 변량효과를 함께 이용하여 더 많은 자연 현상을 설명할 수 있게 되었고, 이를 이용한 최초의 통계적 모형인 혼합효과모형이 소개되었다. 계산기술의 발달과 더불어 복잡한 현상에 대한 추론을 위하여 혼합효과모형은 그 중요성이 더욱 커지고 있다. 이러한 혼합효과모형은 최근 다단계 일반화 선형모형을 포함한 여러 모형으로 확장되었으며, 관측할 수 없는 변량효과를 추론하기 위한 다단계 가능도가 제시되었다. 혼합효과모형 특집호를 통해 이러한 모형들이 여러 통계학적 문제점을 해결하는 과정을 제시하고, 앞으로 어떤 확장이 추가적으로 요구되는 지에 대하여 논할 것이다. 빈도록적 접근법과 베이지안 접근법을 함께 다룬다.

Science has developed with great achievements after Galileo's discovery of the law depicting a relationship between observable variables. However, many natural phenomena have been better explained by models including unobservable random effects. A mixed effect model was the first statistical model that included unobservable random effects. The importance of the mixed effect models is growing along with the advancement of computational technologies to infer complicated phenomena; subsequently mixed effect models have extended to various statistical models such as hierarchical generalized linear models. Hierarchical likelihood has been suggested to estimate unobservable random effects. Our special issue about mixed effect models shows how they can be used in statistical problems as well as discusses important needs for future developments. Frequentist and Bayesian approaches are also investigated.

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참고문헌

  1. Airy, G. B. (1861). On the Algebraic and Numerical Theory of Errors of Observations and the Combination of Observations, Macmillan and Co., Ltd., London.
  2. Bayarri, M. J., DeGroot, M. H. and Kadane, J. B. (1988). What is the likelihood function? (with discussion), Statistical Decision Theory and Related Topics IV, 1, eds S.S. Gupta and J. O. Berger, Springer, New York.
  3. Bayes, T. (1763). An essay towards solving a problem in the doctrine of chances. by the late Rev. Mr. Bayes, FRS. communicated by Mr. Price, in a letter to John Canton, AMFRS, Philosophical Transactions (1683-1775), 370-418.
  4. Benjamini, Y. and Hochberg, Y. (1995). Controlling the false discovery rate: A practical and powerful approach to multiple testing, Journal of the Royal Statistical Society B, 57, 289-300.
  5. Berger, J. O. and Wolpert, R. (1984). The Likelihood Principle, Hayward: Institute of Mathematical Statistics Monograph Series.
  6. Birnbaum, A. (1962). On the foundations of statistical inference, Journal of the American Statistical Association, 57, 269-326 https://doi.org/10.1080/01621459.1962.10480660
  7. Bjørnstad, J. F. (1996). On the generalization of the likelihood function and likelihood principle, Journal of the American Statistical Association, 91, 791-806.
  8. Breslow, N. E. and Clayton, D. (1993). Approximate inference in generalized linear mixed models, Journal of the American Statistical Association, 88, 9-25.
  9. Butler, R. W. (1986). Predictive likelihood inference with applications (with discussion), Journal of the RoyalStatistical Society, Series B, 48, 1-38.
  10. Engle, R. F. (1982). Autoregressive conditional heteroskedasticity with estimates of the variance of U.K. inflation, Econometrica, 50, 987-1008. https://doi.org/10.2307/1912773
  11. Fisher, R. A. (1921). On the probable error of a coefficient of correlation deduced from a small sample, Metron, 1, 3-32.
  12. Ha, I. D., Lee, Y. and Song J.-K. (2001). Hierarchical likelihood approach for frailty models, Biometrika, 88, 233-243. https://doi.org/10.1093/biomet/88.1.233
  13. Ha, I. D., Noh, M. and Lee, Y. (2012). frailtyHL: A package for fitting frailty models with h-likelihood, R Journal, 4, 28-37.
  14. Ha, I. D., Pan, J., Oh, S. and Lee, Y. (2014). Variable selection in general frailty models using penalized h-likelihood, Journal of Computational and Graphical Statistics, 23, 1044-1060. https://doi.org/10.1080/10618600.2013.842489
  15. Lauritzen, S. L. (1974). Sufficiency, prediction and extreme models, Scandinavian Journal of Statistics, 1, 128-134.
  16. Lee, D., Lee, W., Lee, Y. and Pawitan, Y. (2010). Super-sparse principal component analyses for high-throughput genomic data, BMC Bioinformatics, 11, 296. https://doi.org/10.1186/1471-2105-11-296
  17. Lee, D., Lee, W., Lee, Y. and Pawitan, Y. (2011). Sparse partial least-squares regression and its applications to high-throughput data analysis, Chemometrics and Intelligent Laboratory Systems, 109, 1-8 https://doi.org/10.1016/j.chemolab.2011.07.002
  18. Lee, J., Lee, K. and Lee, Y. (2014). History and future of Bayesian statistics, The Korean Journal of Applied Statistics, 27, 855-863. https://doi.org/10.5351/KJAS.2014.27.6.855
  19. Lee, S., Pawitan, Y. and Lee, Y. (2015). A random-effect model approach for group variable selection, Computational Statistics and Data Analysis, 89, 147-157. https://doi.org/10.1016/j.csda.2015.02.020
  20. Lee, Y. and Bjornstad, J. F. (2013). Extended likelihood approach to large scale multiple testing, Journal of the Royal Statistical Society B, 75, 553-575. https://doi.org/10.1111/rssb.12005
  21. Lee, Y. and Nelder, J. A. (1996). Hierarchical generalized linear models (with discussion), Journal of the Royal Statistical Society B, 58, 619-678.
  22. Lee, Y. and Nelder, J. A. (2001). Hierarchical generalised linear models: A synthesis of generalised linear models, random-effect models and structured dispersions, Biometrika, 88, 987-1006. https://doi.org/10.1093/biomet/88.4.987
  23. Lee, Y. and Nelder, J. A. (2006). Double hierarchical generalized linear models (with discussion), Journal of the Royal Statistical Society C, 55, 139-185. https://doi.org/10.1111/j.1467-9876.2006.00538.x
  24. Lee, Y., Nelder, J. A. and Pawitan, Y. (2006). Generalised Linear Models with Random Effects: Unified Analysis via h-Likelihood, Chapman and Hall, London.
  25. Lee, Y. and Noh, M. (2012). Modelling random effect variance with double hierarchical generalized linear models, Statistical Modelling, 12, 487-502. https://doi.org/10.1177/1471082X12460132
  26. Lee, Y. and Oh, H. (2014). A new sparse variable selection via random-effect model, Journal of Multivariate Analysis, 125, 89-99. https://doi.org/10.1016/j.jmva.2013.11.016
  27. Molas, M., Noh, M., Lee, Y. and Lesaffre, E. (2013). Joint hierarchical generalized linear models with multivariate Gaussian random effects, Computational Statistics and Data Analysis, 68, 239-250. https://doi.org/10.1016/j.csda.2013.07.011
  28. Nelder, J. A. and Wedderburn, R. W. M. (1972). Generalized linear models, Journal of the Royal Statistical Society A, 135, 370-384. https://doi.org/10.2307/2344614
  29. Pawitan, Y. (2001). In All Likelihood: Statistical Modelling and Inference using Likelihood, Clarendon Press, Oxford.
  30. Pearson, K. (1920). The fundamental problems of practical statistics, Biometrika, 13, 1-16. https://doi.org/10.1093/biomet/13.1.1
  31. Price, C. J., Kimmel, C. A., Tyle, R. W. and Marr, M. C. (1985). The developmental toxicity of Ethylene Glycol in rates and mice, Toxicological Applications in Pharmacololgy, 81, 113-127.