대한토목학회논문집 (KSCE Journal of Civil and Environmental Engineering Research)

  • 제38권6호
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  • Pages.801-808
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  • 2018
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  • 1015-6348(pISSN)
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  • 2799-9629(eISSN)
대한토목학회 (Korean Society of Civil Engeneers)
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호우피해자료에서의 고차원 자료 및 다중공선성 문제를 해소한 회귀모형 개발

Development of Regression Models Resolving High-Dimensional Data and Multicollinearity Problem for Heavy Rain Damage Data

  • 김정환 (인하대학교 수자원시스템연구소) ;
  • 박지현 (인하대학교 통계학과) ;
  • 최창현 (인하대학교 토목공학과) ;
  • 김형수 (인하대학교 사회인프라공학과)
  • 투고 : 2018.09.04
  • 심사 : 2018.11.13
  • 발행 : 2018.12.01
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초록

선형회귀모형의 학습은 일반적으로 자료의 개수가 설명변수의 개수보다 충분히 크고, 설명변수들 사이에 심각한 다중공선성이 없다는 가정 하에서 안정적으로 이루어진다. 본 연구에서는 이러한 가정이 위배되었을 경우 모형 학습의 어려움을 실제 호우피해자료를 분석함으로써 조명하였고, 이를 해결하기 위해 자료를 통합한 다음 주성분회귀모형 또는 능형회귀모형을 사용할 것을 검토하였다. 모형의 학습에 사용된 자료와 별도의 독립된 자료에서 제안된 모형들의 예측력을 평가하였고, 제안된 방법이 선형회귀모형보다 더 나은 예측력을 보이는 것을 확인하였다.

The learning of the linear regression model is stable on the assumption that the sample size is sufficiently larger than the number of explanatory variables and there is no serious multicollinearity between explanatory variables. In this study, we investigated the difficulty of model learning when the assumption was violated by analyzing a real heavy rain damage data and we proposed to use a principal component regression model or a ridge regression model after integrating data to overcome the difficulty. We evaluated the predictive performance of the proposed models by using the test data independent from the training data, and confirmed that the proposed methods showed better predictive performances than the linear regression model.

키워드

TMHHC2_2018_v38n6_801_f0001.png 이미지

Fig. 1. Sample Sizes of Sigungu

TMHHC2_2018_v38n6_801_f0002.png 이미지

Fig. 2. Correlation Among Explanatory Variables

TMHHC2_2018_v38n6_801_f0003.png 이미지

Fig. 3. Cross-Validation Plot for 

Table 1. Principal Loadings

TMHHC2_2018_v38n6_801_t0001.png 이미지

Table 2. Predictive Performances (Unit: 1,000 KW)

TMHHC2_2018_v38n6_801_t0002.png 이미지

Table 3. Estimated Regression Coefficients

TMHHC2_2018_v38n6_801_t0003.png 이미지

참고문헌

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