October 2021
Intermediate to advanced
289 pages
8h 31m
Chinese
Content preview from 数据科学中的实用统计学(第2版)
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174
｜
第
5
章
5.3.5
系数和优势比的解释
逻辑回归的一个优点是，它生成的模型不需要重新计算就可以快速地为新数据打分。与其
他分类方法相比，它的另一个优点是模型很容易解释。在模型解释中，需要理解的一个关
键概念是
优势比
（
odds ratio
）
。二元因子变量
X
的优势比是最容易理解的：
优势比
Odds( 1| 1)
Odds( 1| 0)
YX
YX
= =
=
= =
这个优势比可以解释为当
X
=
1
时
Y
=
1
的发生比与
X
=
0
时
Y
=
1
的发生比的比值。如果
优势比为
2
，就是说当
X
=
1
时，
Y
=
1
的发生比是
X
=
0
时的
2
倍。
为什么不使用概率，而使用优势比呢？因为逻辑回归中的系数
β
j
就是
X
j
的优势比的对数，
所以选择使用优势比。
下面通过一个例子来辅助理解。在
5.3.2
节中，我们拟合了一个模型，其中
purpose_small_
business
的回归系数是
1.21526
。这个系数的意义是，与贷款目的是还清信用卡相比，贷
款给小型企业会将违约相对于还清的优势比提高
exp(1.21526)
≈
3.4
。显然
，如果贷款目的
是创建或扩展一个小型企业，那么风险就会远远高于其他类型的贷款。
图
5-3
给出了优势比大于
1
时
，优势比与对数优势比之间的关系。因为系数是以对数表示
的，所以系数增加
1
就会使优势比增加
exp(1)
≈
2.72
。
图 5-3：优势比与对数优势比之间的关系
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