# Logistic回归

2017/11/07 08:30

• Logistic回归介绍

Logistic回归适用于二值相应变量（0/1）。模型假设 Y 服从二项分布，线性模型的拟合形式：

glm(Y~X1+X2+X3,family = binomial(link ="logit"),data =mydata)

#使用AER包中的数据框Affairs为例，探究婚外情的回归过程
> data(Affairs,package = "AER")#导入包中的数据，在函数中也有require(包名)
> summary(Affairs)             #先看下描述性统计，知道整体的情况
affairs          gender         age         yearsmarried    children  religiousness     education       occupation
Min.   : 0.000   female:315   Min.   :17.50   Min.   : 0.125   no :171   Min.   :1.000   Min.   : 9.00   Min.   :1.000
1st Qu.: 0.000   male  :286   1st Qu.:27.00   1st Qu.: 4.000   yes:430   1st Qu.:2.000   1st Qu.:14.00   1st Qu.:3.000
Median : 0.000                Median :32.00   Median : 7.000             Median :3.000   Median :16.00   Median :5.000
Mean   : 1.456                Mean   :32.49   Mean   : 8.178             Mean   :3.116   Mean   :16.17   Mean   :4.195
3rd Qu.: 0.000                3rd Qu.:37.00   3rd Qu.:15.000             3rd Qu.:4.000   3rd Qu.:18.00   3rd Qu.:6.000
Max.   :12.000                Max.   :57.00   Max.   :15.000             Max.   :5.000   Max.   :20.00   Max.   :7.000
rating
Min.   :1.000
1st Qu.:3.000
Median :4.000
Mean   :3.932
3rd Qu.:5.000
Max.   :5.000
> table(Affairs$affairs) # 生成交叉表格，会自动统计每类的次数 0 1 2 3 7 12 451 34 17 19 42 38 #Logistic回归是对二值型结果的统计，所以先将数据转化为因子 > Affairs$affairs[Affairs$affairs > 0] <- 1 #[Affairs$affairs > 0]为真时，赋值为1
> Affairs$affairs[Affairs$affairs == 0] <- 0
> Affairs$ynaffair <- factor(Affairs$affairs,levels = c(0,1),labels=c("No,Yes"))  #转化为因子
> table(Affairs\$ynaffair)#在使用table看下结果
No,Yes1 No,Yes2
451     150

#拟合Logistic模型
> fit.full <- glm(ynaffair ~ gender + age + yearsmarried + children +
+                   religiousness + education + occupation +rating,
+                 data=Affairs,family=binomial())
> summary(fit.full)

Call:
glm(formula = ynaffair ~ gender + age + yearsmarried + children +
religiousness + education + occupation + rating, family = binomial(),
data = Affairs)

Deviance Residuals:
Min       1Q   Median       3Q      Max
-1.5713  -0.7499  -0.5690  -0.2539   2.5191

Coefficients:
Estimate Std. Error z value Pr(>|z|)
(Intercept)    1.37726    0.88776   1.551 0.120807
gendermale     0.28029    0.23909   1.172 0.241083       #无“*”号表示不显著，即 p>0.05
age           -0.04426    0.01825  -2.425 0.015301 *     #"*"越多表示越显著
yearsmarried   0.09477    0.03221   2.942 0.003262 **
childrenyes    0.39767    0.29151   1.364 0.172508
religiousness -0.32472    0.08975  -3.618 0.000297 ***
education      0.02105    0.05051   0.417 0.676851
occupation     0.03092    0.07178   0.431 0.666630
rating        -0.46845    0.09091  -5.153 2.56e-07 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

(Dispersion parameter for binomial family taken to be 1)

Null deviance: 675.38  on 600  degrees of freedom
Residual deviance: 609.51  on 592  degrees of freedom
AIC: 627.51

Number of Fisher Scoring iterations: 4

#剔除显著的变量，再拟合
> fit.reduced <- glm(ynaffair ~ age + yearsmarried + religiousness +
+                      rating, data=Affairs, family=binomial())
> summary(fit.reduced)

Call:
glm(formula = ynaffair ~ age + yearsmarried + religiousness +
rating, family = binomial(), data = Affairs)

Deviance Residuals:
Min       1Q   Median       3Q      Max
-1.6278  -0.7550  -0.5701  -0.2624   2.3998

Coefficients:
Estimate Std. Error z value Pr(>|z|)
(Intercept)    1.93083    0.61032   3.164 0.001558 **
age           -0.03527    0.01736  -2.032 0.042127 *
yearsmarried   0.10062    0.02921   3.445 0.000571 ***
religiousness -0.32902    0.08945  -3.678 0.000235 ***
rating        -0.46136    0.08884  -5.193 2.06e-07 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

(Dispersion parameter for binomial family taken to be 1)

Null deviance: 675.38  on 600  degrees of freedom
Residual deviance: 615.36  on 596  degrees of freedom
AIC: 625.36                                              #发现 简单模型的AIC值比之前的模型的要小，说明是可行的，然后我们也可以用anova()对两次拟合模型进行比较

Number of Fisher Scoring iterations: 4

##使用anova()对两个嵌套模型进行比较，广义线性回归使用Chisp（卡方检验）
> anova(fit.full,fit.reduced,test="Chisq")
Analysis of Deviance Table

Model 1: ynaffair ~ gender + age + yearsmarried + children + religiousness +
education + occupation + rating
Model 2: ynaffair ~ age + yearsmarried + religiousness + rating
Resid. Df Resid. Dev Df Deviance Pr(>Chi)
1       592     609.51
2       596     615.36 -4  -5.8474   0.2108   #卡方值不显著（p=0.217）表明四个预测变量的新模型与九个完整预测变量的模型拟合程度一样好

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