응용통계연구 (The Korean Journal of Applied Statistics)

  • 제18권2호
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  • Pages.471-485
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  • 2005
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  • 1225-066X(pISSN)
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  • 2383-5818(eISSN)
한국통계학회 (The Korean Statistical Society)
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RAINDROP PLOT을 이용한 차원축소

Collapsibility Using Raindrop Plot

  • 홍종선 (성균관대학교 경제학부 통계학전공) ;
  • 김범준 (성균관대학교 통계학과) ;
  • 박지용 (성균관대학교 통계학과)
  • Hong C. S. (Department of Statistics, Sungkyunkwan University) ;
  • Kim B. J. (Department of Statistics, Sungkyunkwan University) ;
  • Park J. Y. (Department of Statistics, Sungkyunkwan University)
  • 발행 : 2005.07.01
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초록

범주형 자료분석에서 차원축소(collapsibility)는 오즈비로 설명되었다. 실제의 $2{\times}2{\times}K$ 분할표 자료를 이 이론에 적응시켰을 때 오즈비의 값으로 차원축소가 가능한지의 여부를 판단하기는 어렵다. 오즈비를 시각적으로 표현하는 방법 중에서 Doi, Nakamura와 Yamamoto(2001)가 제안한 Contour plot을 통해서 분할표 자료를 설명하는 것은 가능하지만 차원축소의 가능성을 결정하기에는 한계가 있다. 본 연구에서는 오즈비의 신뢰구간을 시각적으로 표현할 수 있는 방법으로 Barrowman과 Myers(2003)가 제안한 Raindrop plot을 이용하여 $2{\times}2{\times}K$ 분할표 자료를 설명할 수 있으며 동시에 차원축소의 가능성을 판단할 수 있는 방법을 제안하고자 한다.

For categorical data analysis, the collapsibility were explained with the odds ratio (cross-product ratio). When these theories with these odds ratios are applied to real $2{\times}2{\times}K$ contingency tables, it is impossible to decide whether data are collapsible. Among graphical methods to represent odds ratios, Contour plot which is developed by Doi, Nakamura and Yamamoto (2001) could explain the structure of these data, but cannot decide on the collapsibility. In this paper, by using the Raindrop plot proposed by Barrowman and Myers (2003), we suggest an alternative method which can not only explain the structure of data, but also decide on the collapsibility.

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