原文地址 https://stats.idre.ucla.edu/r/dae/logit-regression/ Logit Regression | R data analysis Example

Logistic regression, also called a logit model, is used to model dichotomous outcome variables. In the logit model the log odds of the outcome is modeled as a linear combination of the predictor variables.(简单理解，逻辑斯蒂回归用于二分类结果建模)生词：dichotomous 对立的；二岐的 the log odds of the outcome

数据

探索GRE、GPA、Rank与研究生录取与否的关系，相应变量为二进制数据 GRE: Graduate Record Exam scores GPA: grade point average Rank: prestige of the undergradute institution A researcher is interested in how variables effect admission into graduate school. The response variable, admit/don't admit, is a binary variable. 研究者感兴趣的是这些变量是如何影响研究生录取的。相应变量为一个二进制的变量

 

  
mydata<-read.csv("https://stats.idre.ucla.edu/stat/data/binary.csv")
  
dim(mydata)
  
head(mydata)
  


  
install.packages("skimr")
  
skimr::skim(mydata)
  
sapply(mydata,sd)
  
sapply(mydata,mean)
  
xtabs(~admit+rank,data=mydata)
 

可选择的分析方法

• Logistic regression

• Probit regression

• OLS regression

• Two-group discriminant function analysis

回归拟合

 

  
mydata$rank<-factor(mydata$rank)
  
mylogit<-glm(admit~gre+gpa+rank,data=mydata,family="binomial")
  
summary(mylogit)
  
confint(mylogit)
  
confint.default(mylogit)
  
newdata1<-with(mydata,data.frame(gre=mean(gre),gpa=mean(gpa),rank=factor(1:4)))
  
newdata1
  
newdata1$rankP<-predict(mylogit,newdata=newdata1,type="response")
  
newdata1
  
newdata2<-with(mydata,data.frame(gre=rep(seq(from=200,to=800,length.out=100)),
  
 gpa=mean(gpa),
  
 rank=factor(rep(1:4,each=100))))
  
newdata3_1<-cbind(newdata2,predict(mylogit,newdata=newdata2,type="response"))
  
head(newdata3_1)
  
newdata3_2<-cbind(newdata2,predict(mylogit,newdata=newdata2,type="link",se=TRUE))
  
head(newdata3_2)
  
newdata3_3<-within(newdata3_2,{
  
 PredictedProb<-plogis(fit)
  
 LL<-plogis(fit-(1.96*se.fit))
  
 UL<-plogis(fit+(1.96*se.fit))
  
})
  
head(newdata3_3)
  
library(ggplot2)
  
ggplot(newdata3_3,aes(x=gre,y=PredictedProb))+
  
 geom_ribbon(aes(ymin=LL,ymax=UL,fill=rank),alpha=0.2)+
  
 geom_line(aes(colour=rank),size=1)+
  
 theme_bw()
  
with(mylogit,null.deviance-deviance)
  
with(mylogit,df.null-df.residual)
  
with(mylogit,pchisq(null.deviance-deviance,df.null-df.residual,lower.tail=F))
  
logLik(mylogit)
 

有的结果还不是很明白

需要把原文再多看几遍

需要抽时间看的内容

• apply函数组的用法

• with函数的用法

新学到的函数

• xtabs()函数

 

  
> xtabs(~admit+rank,data=mydata)
  
 rank
  
admit 1 2 3 4
  
 0 28 97 93 55
  
 1 33 54 28 12
 

• pandas中类似的函数 crosstab

  

python实现逻辑斯蒂分类回归的例子

http://dblab.xmu.edu.cn/blog/logistic-regression-in-python/

还有很多其他分析的实例

https://stats.idre.ucla.edu/other/dae/

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小明的数据分析笔记本