4.6 Generalized Linear Models
In Chapter 3, we assumed that the response $Y$is quantitative, and explored the use of least squares linear regression to predict $Y$. Thus far in this chapter, we have instead assumed that $Y$is qualitative. However, we may sometimes be faced with situations in which $Y$is neither qualitative nor quantitative, and so neither linear regression from Chapter 3 nor the classification approaches covered in this chapter is applicable.
As a concrete example, we consider the Bikeshare data set. The response is bikers , the number of hourly users of a bike sharing program in Washington, DC. This response value is neither qualitative nor quantitative: instead, it takes on non-negative integer values, or counts . We will consider counts predicting bikers using the covariates mnth (month of the year), hr (hour of the day, from 0 to 23), workingday (an indicator variable that equals 1 if it is neither a weekend nor a holiday), temp (the normalized temperature, in Celsius), and weathersit (a qualitative variable that takes on one of four possible values: clear; misty or cloudy; light rain or light snow; or heavy rain or heavy snow.)
In the analyses that follow, we will treat mnth , hr , and weathersit as qualitative variables.
Sub-Chapters (하위 목차)
4.6.1 Linear Regression on the Bikeshare Data (자전거 대여 데이터에서의 선형 회귀 적용)
카운트(음수가 불가능한 건수 데이터) 성질을 갖는 대여량에 일반 선형 회귀를 돌렸을 때 발생하는 음수 예측 등 불합리한 점을 확인합니다.
4.6.2 Poisson Regression on the Bikeshare Data (자전거 대여 데이터에서의 포아송 회귀 적용)
카운트 데이터의 속성에 알맞게 부합하는 분포인 포아송(Poisson) 회귀 모델을 적용, 로그 링크 함수를 사용해 효과적인 성능을 얻습니다.
4.6.3 Generalized Linear Models in Greater Generality (보다 넓은 범주의 GLM 일반화 규칙)
응답 패턴 군집(Exponential family) 개념을 통해 포아송, 이항 회귀, 정규 회귀 등이 결국 매개 변수만 다른 통일된 GLM 형식임을 증명합니다.