응용통계연구 (The Korean Journal of Applied Statistics)

  • 제8권2호
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  • Pages.147-161
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  • 1995
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  • 1225-066X(pISSN)
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  • 2383-5818(eISSN)
한국통계학회 (The Korean Statistical Society)
권호 표지

가산자료(count data)의 과산포 검색: 일반화 과정

Overdispersion in count data - a review

  • 김병수 ((120-749) 서울특별시 서대문구 신촌동 134번지, 연세대학교 응용통계학과) ;
  • 오경주 ((110-450) 서울특별시 종로구 원남동 66-21 보령빌딩, 금강기획 마케팅전략연구소) ;
  • 박철용 ((704-701) 대구직할시 달서구 신당동1000번지, 계명대학교 통계학과)
  • 발행 : 1995.09.01
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초록

생검실험에서는 다산을 통해 번식하는 쥐와 같은 설치류 동물들을 실험대상으로 하여 이항분포나 포아송분포 하에서 가산자료(count data)를 많이 생성한다. 다산을 통해 태어난 동물들을 독립적인 실험대상으로 간주하여 자료분석을 하면, 同腹仔 효과로 인해 기존의 평균과 분산사이의 관계를 벗어나는 과산포현상이 종종 나타난다. 이러한 현상을 무시했을 때 모수추정치에 대한 분산을 과소추정하고, 이로 인하여 가설검정에서 낮은 검정력을 갖게 된다. 이러한 문제점을 해결하기 위하여 최근 10년간 과산포현상을 검색하는 통계량들과 과산포를 반영하는 모형들이 제시되었는데, 이를 개관하고 이러한 절차들의 일반화 과정을 자료 유형별로 비교분석한다.

The primary objective of this paper is to review parametric models and test statistics related to overdspersion of count data. Poisson or binomial assumption often fails to explain overdispersion. We reviewed real examples of overdispersion in count data that occurred in toxicological or teratological experiments. We also reviewed several models that were suggested for implementing experiments. We also reviewed several models that were suggested for implementing the extra-binomial variation or hyper-Poisson variability, and we noted how these models were generalized and further developed. The approaches that have been suggested for the overdispersion fall into two broad categories. The one is to develop a parametric model for it, and the other is to assume a particular relationship between the variance and the mean of the response variable and to derive a score test staistics for detecting the overdispersion. Recently, Dean(1992) derived a general score test statistics for detecting overdispersion from the exponential family.

키워드

참고문헌

  1. 통계학연구 v.22 포아송분포로부터 음이향분포로의 이탈에 대한 검정통계량의 확장 이선호
  2. Biometrika v.75 Analysis of one-way layout of count data with negative binomial variation Barnwal,R.K.;Paul,S.R.
  3. Aplied Statistics v.42 Analysis of dose-response data in the presence of extrabinomial variation Boos,D.D.
  4. Journal of Applied Econometrics v.1 Econometric models based on count data:comparisons and applications of some estimators and tests Cameron,A.C.;Trivedi,P.K.
  5. Econometrika v.52 Testing for neglected heterogeneity Chesher,A.
  6. Journal of the American Statistical Association v.80 Testing goodness of fit for the Poisson assumption when observations are not identically distributed Collings,B.J.;Margolin,B.H.
  7. Biometrika v.70 Some remarks on overdispersion Cox,D.R.
  8. Journal of the American Statistical Association v.84 Tests for detecting overdispersion in Poisson regression models Dean,C.;Lawless,J.F.
  9. Journal of the American Statistical Association v.87 Tests for overdispersion in Poisson and binomial regression models Dean,C.
  10. Journal of the American Statistical Association v.81 Double Exponential Families and Their Use in Generalized Linear Regression Efron,B.
  11. Biometrika v.51 The analysis of Poisson regression with an application in virology Gart,J.J.
  12. Journal of the American Statistical Association v.87 Diagnostics for Overdispersion Ganio,L.M.;Schaffer,D.W.
  13. Mutation Research v.41 The distribution of fetal death in control mice and its implications of statistical tests for dominant lethal effects Haseman,J.K.;Soares,E.R.
  14. Biometrics v.35 Analysis of dichotomous response data from certain toxicological experiments Haseman,J.K.;Kupper,L.L.
  15. Communications in Statistics v.A17 Some remarks on locally most powerful unbiased tests for the detection of the mixtures of Poisson or binomial distributions Kim,B.S.
  16. Communications in Statistics v.A21 Some remarks on testing goodness of fit for the Poisson assumption Kim,B.S.;Park,C.
  17. Biometrics v.48 Testing goodness of fit of a multinomial model against overdispersed alternatives Kim,B.S.;Margolin,B.H.
  18. Biometrics v.34 The use of a correlated binomial model for the analysis of certain toxicological experiments Kupper,L.L.;Haseman,J.K.
  19. International Economic Review v.27 Specification test for Poisson regression models Lee,L.F.
  20. Communications in Statistics v.A Tests for detecting overdispersion in Poisson models Lee,S.;Park,C.;Kim,B.S.
  21. Biometrika v.73 Longitudinal data analysis using generalized linear models Liang,K.Y.;Zeger,S.L.
  22. Biometrics v.49 Case studies in binary dispersion Liang,K.Y.;McCullagh,P.
  23. Mutation Research v.272 Assessing overdispersion and dose-response in the male dominant lethal essay Lockhart,A.C.;Piegosch,W.W.;Bishop,J.B.
  24. Generalized Linear Models(second edition) McCullagh,P.;Nelder,J.A.
  25. Proceedings of the National Academy of Sciences v.78 Statistical analysis of the Ames Salmonella/microsome test Margolin,B.H.;Kaplan,N.;Zeiger,E.
  26. Communications in Statistics v.A16 On the beta-correlated binomial distribution-A three parameter generalization of the binomial distribution Paul,S.R.
  27. Biometrika v.53 Testing for homogeneity-Ⅱ. The Poisson distribution Potthoff,R.F.;Whittinghill,M.
  28. Advanced statistical methods in biometric research Rao,C.R.
  29. Environmetrics v.4 Potency measures for developmental toxicity Ryan,L.
  30. Biometrika v.66 Testing the goodness of fit of the binomial distribution Tarone,R.E.
  31. Biometrics v.31 The analysis of binary responses from toxicological experiments involving reproduction and teratogenicity Williams,D.A.