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广义线性回归
> life<-data.frame(
+ X1=c(2.5, 173, 119, 10, 502, 4, 14.4, 2, 40, 6.6,
+ 21.4, 2.8, 2.5, 6, 3.5, 62.2, 10.8, 21.6, 2, 3.4,
+ 5.1, 2.4, 1.7, 1.1, 12.8, 1.2, 3.5, 39.7, 62.4, 2.4,
+ 34.7, 28.4, 0.9, 30.6, 5.8, 6.1, 2.7, 4.7, 128, 35,
+ 2, 8.5, 2, 2, 4.3, 244.8, 4, 5.1, 32, 1.4),
+ X2=rep(c(0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2,
+ 0, 2, 0, 2, 0, 2, 0),
+ c(1, 4, 2, 2, 1, 1, 8, 1, 5, 1, 5, 1, 1, 1, 2, 1,
+ 1, 1, 3, 1, 2, 1, 4)),
+ X3=rep(c(0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1),
+ c(6, 1, 3, 1, 3, 1, 1, 5, 1, 3, 7, 1, 1, 3, 1, 1, 2, 9)),
+ Y=rep(c(0, 1, 0, 1), c(15, 10, 15, 10))
+ )
> glm.sol<-glm(Y~X1+X2+X3, family=binomial, data=life)
> summary(glm.sol)
Call:
glm(formula = Y ~ X1 + X2 + X3, family = binomial, data = life)
Deviance Residuals:
Min 1Q Median 3Q Max
-1.6960 -0.5842 -0.2828 0.7436 1.9292
Coefficients:
Estimate Std. Error z value Pr(>|z|)
(Intercept) -1.696538 0.658635 -2.576 0.010000 **
X1 0.002326 0.005683 0.409 0.682308
X2 -0.792177 0.487262 -1.626 0.103998
X3 2.830373 0.793406 3.567 0.000361 ***
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
(Dispersion parameter for binomial family taken to be 1)
Null deviance: 67.301 on 49 degrees of freedom
Residual deviance: 46.567 on 46 degrees of freedom
AIC: 54.567
Number of Fisher Scoring iterations: 5
可见拟合的效果不好 > pre<-predict(glm.sol, data.frame(X1=5,X2=2,X3=0))
> p<-exp(pre)/(1+exp(pre));p#不接受治疗
1
0.03664087
>
> pre<-predict(glm.sol, data.frame(X1=5,X2=2,X3=1))
> p<-exp(pre)/(1+exp(pre));p#接受治疗
1
0.3920057
>
> step(glm.sol)
Start: AIC=54.57
Y ~ X1 + X2 + X3
Df Deviance AIC
- X1 1 46.718 52.718
<none> 46.567 54.567
- X2 1 49.502 55.502
- X3 1 63.475 69.475
Step: AIC=52.72
Y ~ X2 + X3
Df Deviance AIC
<none> 46.718 52.718
- X2 1 49.690 53.690
- X3 1 63.504 67.504
Call: glm(formula = Y ~ X2 + X3, family = binomial, data = life)
Coefficients:
(Intercept) X2 X3
-1.642 -0.707 2.784
Degrees of Freedom: 49 Total (i.e. Null); 47 Residual
Null Deviance: 67.3
Residual Deviance: 46.72 AIC: 52.72
> glm.new<-update(glm.sol, .~.-X1)
> summary(glm.new)
Call:
glm(formula = Y ~ X2 + X3, family = binomial, data = life)
Deviance Residuals:
Min 1Q Median 3Q Max
-1.6849 -0.5949 -0.3033 0.7442 1.9073
Coefficients:
Estimate Std. Error z value Pr(>|z|)
(Intercept) -1.6419 0.6381 -2.573 0.010082 *
X2 -0.7070 0.4282 -1.651 0.098750 .
X3 2.7844 0.7797 3.571 0.000355 ***
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
(Dispersion parameter for binomial family taken to be 1)
Null deviance: 67.301 on 49 degrees of freedom
Residual deviance: 46.718 on 47 degrees of freedom
AIC: 52.718
Number of Fisher Scoring iterations: 5
>
> pre<-predict(glm.sol, data.frame(X1=5,X2=2,X3=0))
> p<-exp(pre)/(1+exp(pre));p#不接受治疗
1
0.03664087
>
> pre<-predict(glm.sol, data.frame(X1=5,X2=2,X3=1))
> p<-exp(pre)/(1+exp(pre));p#接受治疗
1
0.3920057
#####再来看一个类似的问题 install.packages('AER') data(Affairs,package='AER')#婚外情数据，包括9个变量，婚外斯通频率，性别，婚龄等。 summary(Affairs) table(Affairs$affairs) #我们感兴趣的是是否有过婚外情所以做如下处理 Affairs$ynaffair[Affairs$affairs>0]<-1 Affairs$ynaffair[Affairs$affairs==0]<-0 Affairs$ynaffair<-factor(Affairs$ynaffair,levels=c(0,1),labels=c('NO','YES')) table(Affairs$ynaffair) #接下来做逻辑回归 fit.full=glm(ynaffair~.-affairs,data=Affairs,family=binomial()) summary(fit.full) #除掉较大p值所对应的变量，如性别，是否有孩子、学历和职业在做一次分析 fit.reduced=glm(ynaffair~age+yearsmarried+religiousness+rating,data=Affairs,family=binomial()) summary(fit.reduced) AIC(fit.full,fit.reduced)#模型比较 #系数解释 exp(coef(fit.reduced))
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