The Korean Journal of Applied Statistics (응용통계연구)

The Korean Statistical Society (한국통계학회)
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The EM algorithm for mixture regression with missing covariates

결측 공변량을 갖는 혼합회귀모형에서의 EM 알고리즘

  • Kim, Hyungmin (Department of Statistics, Sungkyunkwan University) ;
  • Ham, Geonhee (Center for Public Opinion and Quantitative Research, The Asan Institute for Policy Studies) ;
  • Seo, Byungtae (Department of Statistics, Sungkyunkwan University)
  • Received : 2016.08.31
  • Accepted : 2016.10.22
  • Published : 2016.12.31
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Abstract

Finite mixtures of regression models provide an effective tool to explore a hidden functional relationship between a response variable and covariates. However, it is common in practice that data are not fully observed due to several reasons. In this paper, we derived an expectation-maximization (EM) algorithm to obtain the maximum likelihood estimator when some covariates are missing at random in the finite mixture of regression models. We conduct some simulation studies and we also provide some real data examples to show the validity of the derived EM algorithm.

혼합회귀모형은 반응 변수와 공변량 사이의 관계를 규명하는 유용한 통계적 모형으로 여러 분야에서 사용되어지고 있다. 하지만 실제로 혼합회귀모형을 이용하여 분석을 하는 과정에서 공변량이 결측값을 포함하는 문제는 흔하게 발생하며, 발생하는 결측의 유형 또한 다양하게 나타난다. 이러한 경우에 있어서 본 논문에서는 최대우도추정량을 구하기 위한 EM 알고리즘을 제안하고자 한다. 제안된 EM 알고리즘의 효용성을 모의실험을 통해 확인하였으며 또한 사례연구를 통해 제시된 방법이 어떻게 사용될수 있는지와 그 효용성을 함께 확인하였다.

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References

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