The Korean Journal of Applied Statistics (응용통계연구)

The Korean Statistical Society (한국통계학회)
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Principal Components Logistic Regression based on Robust Estimation

로버스트추정에 바탕을 둔 주성분로지스틱회귀

  • 김부용 (숙명여자대학교 통계학과) ;
  • 강명욱 (숙명여자대학교 통계학과) ;
  • 장혜원 ((주)피스트글로벌 종합리스크사업팀)
  • Published : 2009.06.30
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Abstract

Logistic regression is widely used as a datamining technique for the customer relationship management. The maximum likelihood estimator has highly inflated variance when multicollinearity exists among the regressors, and it is not robust against outliers. Thus we propose the robust principal components logistic regression to deal with both multicollinearity and outlier problem. A procedure is suggested for the selection of principal components, which is based on the condition index. When a condition index is larger than the cutoff value obtained from the model constructed on the basis of the conjoint analysis, the corresponding principal component is removed from the logistic model. In addition, we employ an algorithm for the robust estimation, which strives to dampen the effect of outliers by applying the appropriate weights and factors to the leverage points and vertical outliers identified by the V-mask type criterion. The Monte Carlo simulation results indicate that the proposed procedure yields higher rate of correct classification than the existing method.

로지스틱회귀분석은 고객관계관리를 위한 데이터마이닝 분야에서 많이 사용되는 기법인데, 이 분야의 모형설정 과정에서는 연관성이 매우 높은 설명변수들이 모형에 함께 포함되어 다중공선성의 문제를 유발하며, 더욱이 회귀자료에 이상점들이 포함되면 최우추정량은 심각한 결함을 갖게 된다. 두 가지 문제점을 동시에 해결하기 위하여 로버스트주성분로지스틱회귀를 적용할 수 있는데, 본 논문에서는 주성분의 선정기준을 결정하는 모형을 개발하고, 주성분모형에서의 추정치에 미치는 이상점의 영향을 축소하기 위한 로버스트추정법을 제안하였다. 제안된 추정법은 다중공선성과 이상점이 유발하는 문제들을 적절히 해결해 준다는 사실이 모의실험을 통하여 확인되었다.

Keywords

References

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