응용통계연구 (The Korean Journal of Applied Statistics)

  • 제30권6호
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  • Pages.957-981
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  • 2017
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  • 1225-066X(pISSN)
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  • 2383-5818(eISSN)
한국통계학회 (The Korean Statistical Society)
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로지스틱 임의선형 혼합모형의 최대우도 추정법

Maximum likelihood estimation of Logistic random effects model

  • 김민아 (덕성여자대학교 정보통계학과) ;
  • 경민정 (덕성여자대학교 정보통계학과)
  • Kim, Minah (Department of Statistics, Duksung Women's University) ;
  • Kyung, Minjung (Department of Statistics, Duksung Women's University)
  • 투고 : 2017.10.10
  • 심사 : 2017.11.30
  • 발행 : 2017.12.31
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초록

관측되지 않는 효과 또는 고정효과로 설명할 수 없는 분산 구조가 포함되어 정확한 모수 추정이 어려운 경우 체계적인 분석을 위해 일반화 선형 모형은 임의효과가 포함된 일반화 선형 혼합 모형으로 확장되었다. 본 연구에서는 일반화 선형 모형 중에서도 이분적인 반응변수를 다루는 로지스틱 회귀모형에 임의효과를 포함한 최대 우도 추정 방법을 설명한다. 그중에서도 라플라스 근사법, 가우스-에르미트 구적법, 적응 가우스-에르미트 구적법 그리고 유사가능도 우도에 대한 최대우도 추정법을 자세히 알아본다. 또한 제안한 방법을 사용하여 한국 복지 패널 데이터에서 정신건강과 생활만족도가 자원봉사활동에 미치는 영향에 대해 분석한다.

A generalized linear mixed model is an extension of a generalized linear model that allows random effect as well as provides flexibility in developing a suitable model when observations are correlated or when there are other underlying phenomena that contribute to resulting variability. We describe maximum likelihood estimation methods for logistic regression models that include random effects - the Laplace approximation, Gauss-Hermite quadrature, adaptive Gauss-Hermite quadrature, and pseudo-likelihood. Applications are provided with social science problems by analyzing the effect of mental health and life satisfaction on volunteer activities from Korean welfare panel data; in addition, we observe that the inclusion of random effects in the model leads to improved analyses with more reasonable inferences.

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