The Korean Journal of Applied Statistics (응용통계연구)

The Korean Statistical Society (한국통계학회)
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Log-density Ratio with Two Predictors in a Logistic Regression Model

로지스틱 회귀모형에서 이변량 정규분포에 근거한 로그-밀도비

  • 강명욱 (숙명여자대학교 통계학과) ;
  • 윤재은 (숙명여자대학교 통계학과)
  • Received : 2012.11.27
  • Accepted : 2013.01.18
  • Published : 2013.02.28
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Abstract

We present methods for studying the log-density ratio that enables the selection of the predictors and the form to be included in the logistic regression model. Under bivariate normal distributional assumptions, we investigate the form of the log-density ratio as a function of two predictors. If two covariance matrices are equal, then the crossproduct and quadratic terms are not needed. If the variables are uncorrelated, we do not need the crossproduct terms, but we still need the linear and quadratic terms. We also explore other conditions in which the crossproduct and quadratic terms are not needed in the logistic regression model.

로지스틱회귀모형에서 두 설명변수의 조건부 분포가 모두 이변량 정규분포라고 할 수 있다면 설명변수들의 함수로 표현되는 로그-밀도비를 통해 모형에 포함시켜야하는 항을 알 수 있다. 두개의 이변량 정규분포에서 분산-공분산행렬이 같은 경우에는 이차항과 교차항 없이 일차항만으로 충분하다. 상관계수가 모두 0이면 교차항은 설명변수의 분산과 관계없이 필요하지 않다. 또한 로지스틱회귀모형에서 로그-밀도비를 통해 이차항과 교차항이 필요하지 않게 되는 다른 조건들도 알아본다.

Keywords

References

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