Communications for Statistical Applications and Methods

The Korean Statistical Society (한국통계학회)
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Variable Selection with Log-Density in Logistic Regression Model

로지스틱회귀모형에서 로그-밀도비를 이용한 변수의 선택

  • 강명욱 (숙명여자대학교 통계학과) ;
  • 신은영 (숙명여자대학교 통계학과)
  • Received : 20111100
  • Accepted : 20111200
  • Published : 2012.01.30
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Abstract

We present methods to study the log-density ratio of the conditional densities of the predictors given the response variable in the logistic regression model. This allows us to select which predictors are needed and how they should be included in the model. If the conditional distributions are skewed, the distributions can be considered as gamma distributions. A simulation study shows that the linear and log terms are required in general. If the conditional distributions of xjy for the two groups overlap significantly, we need both the linear and log terms; however, only the linear or log term is needed in the model if they are well separated.

로지스틱회귀모형에서 반응변수가 주어졌을 때 설명변수의 조건부 확률분포의 로그-밀도비는 어떤 설명변수가어떻게모형에포함되는지에대한변수선택문제에서유용한정보를제공한다. 설명변수의 조건부 확률분포가 좌우대칭이 아닌 경우 감마분포로 가정하는 것이 적절하다. 여러 가지 모의실험을 수행한 결과를 보면, $x{\mid}y$ = 0과 $x{\mid}y$ = 1의 두 분포가 겹치는 경우에서는 x항과 log(x)항 모두 필요하다. 그리고 두 분포가 분리된 경우에는 x항 또는 log(x)항 중 하나만 필요하다.

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References

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  1. Log-density Ratio with Two Predictors in a Logistic Regression Model vol.26, pp.1, 2013, https://doi.org/10.5351/KJAS.2013.26.1.141