Unit 3 Logistic Regression
这一章主要介绍了Logistic Regression，这里回顾下基本操作。
课程地址：
https://www.edx.org/course/the-analytics-edge
读取数据
setwd("E:\\The Analytics Edge\\Unit 3 Logistic Regression")
framingham = read.csv("framingham.csv")Randomly split the data into training and testing sets
library(caTools)
set.seed(1000)
split = sample.split(framingham$TenYearCHD, SplitRatio = 0.65)划分测试集，训练集
train = subset(framingham, split==TRUE)
test = subset(framingham, split==FALSE)Logistic Regression Model
R中使用Logistic Regression的方法很简单，只要使用如下的格式。
framinghamLog = glm(TenYearCHD ~ ., data = train, family=binomial)
summary(framinghamLog)Call:
glm(formula = TenYearCHD ~ ., family = binomial, data = train)
Deviance Residuals:
Min 1Q Median 3Q Max
-1.8487 -0.6007 -0.4257 -0.2842 2.8369
Coefficients:
Estimate Std. Error z value Pr(>|z|)
(Intercept) -7.886574 0.890729 -8.854 < 2e-16 ***
male 0.528457 0.135443 3.902 9.55e-05 ***
age 0.062055 0.008343 7.438 1.02e-13 ***
education -0.058923 0.062430 -0.944 0.34525
currentSmoker 0.093240 0.194008 0.481 0.63080
cigsPerDay 0.015008 0.007826 1.918 0.05514 .
BPMeds 0.311221 0.287408 1.083 0.27887
prevalentStroke 1.165794 0.571215 2.041 0.04126 *
prevalentHyp 0.315818 0.171765 1.839 0.06596 .
diabetes -0.421494 0.407990 -1.033 0.30156
totChol 0.003835 0.001377 2.786 0.00533 **
sysBP 0.011344 0.004566 2.485 0.01297 *
diaBP -0.004740 0.008001 -0.592 0.55353
BMI 0.010723 0.016157 0.664 0.50689
heartRate -0.008099 0.005313 -1.524 0.12739
glucose 0.008935 0.002836 3.150 0.00163 **
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
(Dispersion parameter for binomial family taken to be 1)
Null deviance: 2020.7 on 2384 degrees of freedom
Residual deviance: 1792.3 on 2369 degrees of freedom
(371 observations deleted due to missingness)
AIC: 1824.3
Number of Fisher Scoring iterations: 5
Predictions on the test set
在测试集上预测结果。
predictTest = predict(framinghamLog, type="response", newdata=test)Confusion matrix with threshold of 0.5
设置threshold为$0.5$，比较结果。
table(test$TenYearCHD, predictTest > 0.5) FALSE TRUE
0 1069 6
1 187 11
Compute Outcome Measures
这里介绍一下评价模型的Confusion Matrix。
这里比较重要的是Sensitivity和Specificity，对threshold取不同的值，可以得到不同的Sensitivity和Specificity，这样得到的图像叫做Receiver Operator Characteristic (ROC)曲线，下面介绍如何画ROC曲线。
Plot ROC curve
library(ROCR)
ROCRpred = prediction(predictTest, test$TenYearCHD)
ROCRperf = performance(ROCRpred, "tpr", "fpr")
plot(ROCRperf, colorize=TRUE, print.cutoffs.at=seq(0,1,by=0.1), text.adj=c(-0.2,1.7))
Area Under the ROC Curve (AUC)
最后介绍一下AUC，AUC表示ROC曲线围成的面积，如下图所示：
AUC表示随机给一个positive和negative的案例，我们预测正确的比例，可以如下计算。
as.numeric(performance(ROCRpred, "auc")@y.values)0.742109466760632
将threshold设置为AUC。
table(test$TenYearCHD, predictTest > 0.742109466760632) FALSE
0 1075
1 198
Use multiple Imputation to deal with missing data
补充处理缺失值的方法。
polling = read.csv("PollingData.csv")
summary(polling) State Year Rasmussen SurveyUSA
Arizona : 3 Min. :2004 Min. :-41.0000 Min. :-33.0000
Arkansas : 3 1st Qu.:2004 1st Qu.: -8.0000 1st Qu.:-11.7500
California : 3 Median :2008 Median : 1.0000 Median : -2.0000
Colorado : 3 Mean :2008 Mean : 0.0404 Mean : -0.8243
Connecticut: 3 3rd Qu.:2012 3rd Qu.: 8.5000 3rd Qu.: 8.0000
Florida : 3 Max. :2012 Max. : 39.0000 Max. : 30.0000
(Other) :127 NA's :46 NA's :71
DiffCount PropR Republican
Min. :-19.000 Min. :0.0000 Min. :0.0000
1st Qu.: -6.000 1st Qu.:0.0000 1st Qu.:0.0000
Median : 1.000 Median :0.6250 Median :1.0000
Mean : -1.269 Mean :0.5259 Mean :0.5103
3rd Qu.: 4.000 3rd Qu.:1.0000 3rd Qu.:1.0000
Max. : 11.000 Max. :1.0000 Max. :1.0000
可以看到有一些缺失值，把有缺失值的列单独取出。
library(mice)
simple = polling[c("Rasmussen", "SurveyUSA", "PropR", "DiffCount")]
summary(simple) Rasmussen SurveyUSA PropR DiffCount
Min. :-41.0000 Min. :-33.0000 Min. :0.0000 Min. :-19.000
1st Qu.: -8.0000 1st Qu.:-11.7500 1st Qu.:0.0000 1st Qu.: -6.000
Median : 1.0000 Median : -2.0000 Median :0.6250 Median : 1.000
Mean : 0.0404 Mean : -0.8243 Mean :0.5259 Mean : -1.269
3rd Qu.: 8.5000 3rd Qu.: 8.0000 3rd Qu.:1.0000 3rd Qu.: 4.000
Max. : 39.0000 Max. : 30.0000 Max. :1.0000 Max. : 11.000
NA's :46 NA's :71
可以用如下方法处理缺失值。
imputed = complete(mice(simple))
summary(imputed) Rasmussen SurveyUSA PropR DiffCount
Min. :-41.000 Min. :-33.000 Min. :0.0000 Min. :-19.000
1st Qu.: -8.000 1st Qu.:-11.000 1st Qu.:0.0000 1st Qu.: -6.000
Median : 3.000 Median : 1.000 Median :0.6250 Median : 1.000
Mean : 1.703 Mean : 2.014 Mean :0.5259 Mean : -1.269
3rd Qu.: 10.000 3rd Qu.: 18.000 3rd Qu.:1.0000 3rd Qu.: 4.000
Max. : 39.000 Max. : 30.000 Max. :1.0000 Max. : 11.000
polling$Rasmussen = imputed$Rasmussen
polling$SurveyUSA = imputed$SurveyUSA
summary(polling) State Year Rasmussen SurveyUSA
Arizona : 3 Min. :2004 Min. :-41.000 Min. :-33.000
Arkansas : 3 1st Qu.:2004 1st Qu.: -8.000 1st Qu.:-11.000
California : 3 Median :2008 Median : 3.000 Median : 1.000
Colorado : 3 Mean :2008 Mean : 1.703 Mean : 2.014
Connecticut: 3 3rd Qu.:2012 3rd Qu.: 10.000 3rd Qu.: 18.000
Florida : 3 Max. :2012 Max. : 39.000 Max. : 30.000
(Other) :127
DiffCount PropR Republican
Min. :-19.000 Min. :0.0000 Min. :0.0000
1st Qu.: -6.000 1st Qu.:0.0000 1st Qu.:0.0000
Median : 1.000 Median :0.6250 Median :1.0000
Mean : -1.269 Mean :0.5259 Mean :0.5103
3rd Qu.: 4.000 3rd Qu.:1.0000 3rd Qu.:1.0000
Max. : 11.000 Max. :1.0000 Max. :1.0000
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