Communications for Statistical Applications and Methods

The Korean Statistical Society (한국통계학회)
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Statistical Modeling of Learning Curves with Binary Response Data

이항 반응 자료에 대한 학습곡선의 모형화

  • Lee, Seul-Ji (Department of Statistics, Sungshin Women's University) ;
  • Park, Man-Sik (Department of Statistics, Sungshin Women's University)
  • 이슬지 (성신여자대학교 통계학과) ;
  • 박만식 (성신여자대학교 통계학과)
  • Received : 2012.03.14
  • Accepted : 2012.04.19
  • Published : 2012.05.31
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Abstract

As a worker performs a certain operation repeatedly, he tends to become familiar with the job and complete it in a very short time. That means that the efficiency is improved due to his accumulated knowledge, experience and skill in regards to the operation. Investing time in an output is reduced by repeating any operation. This phenomenon is referred to as the learning curve effect. A learning curve is a graphical representation of the changing rate of learning. According to previous literature, learning curve effects are determined by subjective pre-assigned factors. In this study, we propose a new statistical model to clarify the learning curve effect by means of a basic cumulative distribution function. This work mainly focuses on the statistical modeling of binary data. We employ the Newton-Raphson method for the estimation and Delta method for the construction of confidence intervals. We also perform a real data analysis.

연구자가 같은 작업을 반복적으로 수행할 때, 작업 효율성은 연구에 관련된 지식, 경험, 기술이 축적되면서 향상된다. 결과를 얻기 위해 연구에 투자하는 시간은 같은 작업을 반복함으로써 줄일 수 있다. 이러한 현상을 학습곡선 효과(learning curve effect)라고 일컫는다. 학습곡선(learning curves)은 학습의 변화를 시각적으로 나타낸 것으로 이전의 학습곡선 연구에서는 시간을 일정한 구간으로 나누어 구간별 작업에 대한 숙련도의 평균 차이 여부를 확인하였다. 이러한 방법은 구간을 어떻게 나눌 것인가 하는 기준이 존재하지 않으며, 더욱이 이항 반응 자료로 모형을 적합하기 어려운 문제점을 가지고 있다. 본 연구에서는 이산형 확률변수 중 이항 반응 자료(베르누이자료)에 대한 학습곡선의 통계적 모형에 초점을 맞추고자 한다. 누적확률분포의 특성을 이용하여 모수를 추정하기 위해서 뉴튼-랩슨 방법(Newton-Raphson method)을 사용하였고, 이 연구에서 제안한 모형의 점근적 분포를 구하였다.

Keywords

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