Logistic regression tips: different kinds of regressions

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This post is about different kinds of regressions and their differences.

Binomial logistic regression

又名logit model。传统的逻辑回归,因变量为二值属性,可以扩展到多值逻辑回归(motinomial logistic regression),通过将因变量进行one-hot操作即可(coefficient的增加和log odds的增加一致,详情参见reference #1)。

通过调用R语言中glm函数,设置family参数为binomial即可实现二值逻辑回归的函数调用。

Motinomial logistic regression

又名polytomous LR(多义逻辑回归),multiclass LR,softmax regression,multinomial logit(mlogit),maximum entropy (MaxEnt) classifier,conditional maximum entropy model。是上述二值逻辑回归的拓展,因变量为无序的离散变量(categorical variable/nominal)。

与binomial logistic regression不同的是,MLR的公式左侧不是odds的log值,而是有一个base-level(pivot),其他的几个level计算基于pivot的回归。如下面的公式所示:

因此,得到的结果中coefficient的值不指向log odds的变化,而是因变量中某个level发生概率与base-level发生概率的比值的log值的变化。

to be continued…

Multinomial probit regression

Multiple-group discriminant function analysis

Multiple logistic regression analyses

Ordinal logistic regression

references

Wikipedia: Logistic regression

Wikipedia: multinomial logistic regression

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