Journal of the Korean Data and Information Science Society

The Korean Data and Information Science Society (한국데이터정보과학회)
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Graphical regression and model assessment in logistic model

로지스틱모형에서 그래픽을 이용한 회귀와 모형평가

  • Kahng, Myung-Wook (Department of Statistics, Sookmyung Women's University) ;
  • Kim, Bu-Yong (Department of Statistics, Sookmyung Women's University) ;
  • Hong, Ju-Hee (Department of Statistics, Sookmyung Women's University)
  • 강명욱 (숙명여자대학교 통계학과) ;
  • 김부용 (숙명여자대학교 통계학과) ;
  • 홍주희 (숙명여자대학교 통계학과)
  • Published : 2010.01.31
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Abstract

Graphical regression is a paradigm for obtaining regression information using plots without model assumptions. The general goal of this approach is to find lowdimensional sufficient summary plots without loss of important information. Model assessments using residual plots are less likely to be successful in models that are not linear. As an alternative approach, marginal model plots provide a general graphical method for assessing the model. We apply the methods of graphical regression and model assessment using marginal model plots to the logistic regression model.

그래픽적 회귀는 모형에 대한 가정을 하지 않고 회귀정보를 모두 포함하는 충분요약그림을 찾아내는 분석 방법으로 모든 회귀정보를 저차원의 그림으로 표현할 수 있게 하는 데에 그 목적이 있다. 잔차산점도를 이용한 모형의 평가는 적용 범위가 선형회귀모형에 국한되는 문제점이 있기 때문에 일반화선형모형에서는 그 대안으로 주변모형 산점도를 이용하여 모형의 적절성을 평가한다. 본 논문에서는 일반화선형모형 중에서 이진반응변수를 갖는 로지스틱모형에서의 그래픽적 회귀 방법과 주변모형 산점도를 이용한 모형평가 방법을 알아본다.

Keywords

References

  1. Atkinson, A. C. (1985). Plots, transformations, and regression, Oxford University Press, Oxford.
  2. Azzalini, A. and Bowman, A. W. (1993). On the use of nonparametric regression for checking linear relationships. Journal of the Royal Statistical Society, Ser. B, 55, 549-557.
  3. Chambers, J. M., Cleveland, W. S., Kleiner, B. and Tukey, P. (1983). Graphical methods for data Analysis, Chapman and Hall, New York.
  4. Cleveland, W. and Devlin, D. J. (1988). Locally weighted regression: An approach to regression analysis by local fitting. Journal of the American Statistical Association, 83, 596-610. https://doi.org/10.2307/2289282
  5. Cleveland, W. S. (1987). Research in statistical graphics. Journal of the American Statistical Association, 82, 419-423. https://doi.org/10.2307/2289443
  6. Cook, R. D. (1998). Regression graphics: Idea for studying regressions through graphics, John Wiley & Sons, New York.
  7. Cook, R. D. and Weisberg, S. (1982). Residuals and influence in regression, Chapman and Hall, New York.
  8. Cook, R. D. and Weisberg, S. (1994). An introduction to regression graphics, John Wiley & Sons, New York.
  9. Cook, R. D. and Weisberg, S. (1997). Graphics for assessing the adequacy of regression models. Journal of the American Statistical Association, 92, 490-499. https://doi.org/10.2307/2965698
  10. Cook, R. D. and Weisberg, S. (1999). Applied regression including computing and graphics, John Wiley & Sons, New York.
  11. Ezekiel, M. (1924). A method for handling curvilinear correlation for any number of variables. Journal of the American Statistical Association, 19, 431-453. https://doi.org/10.2307/2281561
  12. Kahng, M. (2005). Exploring interaction in generalized linear models. Journal of Korean Data & Information Science Society, 16, 13-18.
  13. Kahng, M. and Kim, M. (2004). A score test for detection of outliers in generalized linear models. Journal of Korean Data & Information Science Society, 15, 129-139.
  14. Lee, J. and Rhee, S. (2003). Logistic model for normality by neural networks. Journal of Korean Data & Information Science Society, 14, 119-129.
  15. Seo, M. and Kim, J. (2006). Estimation of odds ratio in proportional odds model. Journal of Korean Data & Information Science Society, 17, 1067-1076.
  16. Tierney, L. (1990). Lisp-Stat: An object-oriented environment for statistical computing and dynamic graphics, John Wiley & Sons, New York.
  17. Weisberg, S. (2005). Applied linear regression, 3rd Ed., John Wiley & Sons, New York.