Customer Churn Prediction
Luqi Yao
Loading packages that will be used in the project
library(glmnet)
library(boot)
library(caret)
library(popbio)
library(pROC)
library(rpart)
library(rattle)
library(dplyr)
library(lattice)
library(ggplot2)Loading and exploring data
churndata <- read.csv('/Users/youluqi/webdata/churn.csv')
summary(churndata)## State Account.Length Area.Code Phone Int.l.Plan
## WV : 106 Min. : 1.0 Min. :408.0 327-1058: 1 no :3010
## MN : 84 1st Qu.: 74.0 1st Qu.:408.0 327-1319: 1 yes: 323
## NY : 83 Median :101.0 Median :415.0 327-3053: 1
## AL : 80 Mean :101.1 Mean :437.2 327-3587: 1
## OH : 78 3rd Qu.:127.0 3rd Qu.:510.0 327-3850: 1
## OR : 78 Max. :243.0 Max. :510.0 327-3954: 1
## (Other):2824 (Other) :3327
## VMail.Plan VMail.Message Day.Mins Day.Calls
## no :2411 Min. : 0.000 Min. : 0.0 Min. : 0.0
## yes: 922 1st Qu.: 0.000 1st Qu.:143.7 1st Qu.: 87.0
## Median : 0.000 Median :179.4 Median :101.0
## Mean : 8.099 Mean :179.8 Mean :100.4
## 3rd Qu.:20.000 3rd Qu.:216.4 3rd Qu.:114.0
## Max. :51.000 Max. :350.8 Max. :165.0
##
## Day.Charge Eve.Mins Eve.Calls Eve.Charge
## Min. : 0.00 Min. : 0.0 Min. : 0.0 Min. : 0.00
## 1st Qu.:24.43 1st Qu.:166.6 1st Qu.: 87.0 1st Qu.:14.16
## Median :30.50 Median :201.4 Median :100.0 Median :17.12
## Mean :30.56 Mean :201.0 Mean :100.1 Mean :17.08
## 3rd Qu.:36.79 3rd Qu.:235.3 3rd Qu.:114.0 3rd Qu.:20.00
## Max. :59.64 Max. :363.7 Max. :170.0 Max. :30.91
##
## Night.Mins Night.Calls Night.Charge Intl.Mins
## Min. : 23.2 Min. : 33.0 Min. : 1.040 Min. : 0.00
## 1st Qu.:167.0 1st Qu.: 87.0 1st Qu.: 7.520 1st Qu.: 8.50
## Median :201.2 Median :100.0 Median : 9.050 Median :10.30
## Mean :200.9 Mean :100.1 Mean : 9.039 Mean :10.24
## 3rd Qu.:235.3 3rd Qu.:113.0 3rd Qu.:10.590 3rd Qu.:12.10
## Max. :395.0 Max. :175.0 Max. :17.770 Max. :20.00
##
## Intl.Calls Intl.Charge CustServ.Calls Churn.
## Min. : 0.000 Min. :0.000 Min. :0.000 False.:2850
## 1st Qu.: 3.000 1st Qu.:2.300 1st Qu.:1.000 True. : 483
## Median : 4.000 Median :2.780 Median :1.000
## Mean : 4.479 Mean :2.765 Mean :1.563
## 3rd Qu.: 6.000 3rd Qu.:3.270 3rd Qu.:2.000
## Max. :20.000 Max. :5.400 Max. :9.000
## Data clearning. Delete columns which cannot be used for prediction, such as Phone and State. Then convert char variables to factors.
churndata_1 <- select(churndata, -Phone,-State)
churndata_1$Int.l.Plan <- ifelse(churndata_1$Int.l.Plan=='no',0,1)
churndata_1$VMail.Plan <- ifelse(churndata_1$VMail.Plan=='no',0,1)Logistic Regression Model
The LASSO (Least Absolute Shrinkage and Selection Operator) is a regression method that involves penalizing the absolute size of the regression coefficients. By penalizing, you end up in a situation where some of the parameter estimates may be exactly zero. The larger the penalty applied, the further estimates are shrunk towards zero. This is convenient for variable selection.
Now I’m going to use glmnet package to fit lasso for logistic regression model.
x <- as.matrix(churndata_1[,1:18])
y <- as.matrix(churndata_1[,19])
LASSO_model <- cv.glmnet(x,y,family="binomial",type.measure="deviance")
plot(LASSO_model)
The left line corresponds to the model with best lamda value. The right line shows the best model within 1 standard error.
Here is the largest value of lambda.
LASSO_model$lambda.1se## [1] 0.01714012A fitted logistic regression for the full data:
final_model <- LASSO_model$glmnet.fitCoefficients of the regression model:
model.coef <- coef(LASSO_model$glmnet.fit,s=LASSO_model$lambda.1se)
model.coef## 19 x 1 sparse Matrix of class "dgCMatrix"
## 1
## (Intercept) -4.845358683
## Account.Length .
## Area.Code .
## Int.l.Plan 1.539177233
## VMail.Plan -0.400587947
## VMail.Message .
## Day.Mins 0.008677193
## Day.Calls .
## Day.Charge .
## Eve.Mins 0.002750365
## Eve.Calls .
## Eve.Charge .
## Night.Mins .
## Night.Calls .
## Night.Charge .
## Intl.Mins 0.014800977
## Intl.Calls -0.007744837
## Intl.Charge 0.003849372
## CustServ.Calls 0.354297111Prediction
Make prediction on the whole dataset. Two types of output has been introduced here.
LASSO_pre <- predict(final_model,newx = x, s=LASSO_model$lambda.1se,type = 'response')
head(LASSO_pre)## 1
## [1,] 0.12861786
## [2,] 0.05963995
## [3,] 0.09574063
## [4,] 0.55501055
## [5,] 0.43729223
## [6,] 0.33011944LASSO_pre_class <- predict(final_model,newx = x, s=LASSO_model$lambda.1se,type = 'class')
head(LASSO_pre_class)## 1
## [1,] "False."
## [2,] "False."
## [3,] "False."
## [4,] "True."
## [5,] "False."
## [6,] "False."Visualization of Regression Results
churndata_1$Churn1 = ifelse(churndata_1$Churn.=='True.',1,0)
popbio::logi.hist.plot(churndata_1$Day.Charge, churndata_1$Churn1, boxp=FALSE,type="hist",col="gray")
Model Evalution
1. ConfusionMatrix
table(y,LASSO_pre_class)## LASSO_pre_class
## y False. True.
## False. 2820 30
## True. 443 40confusionMatrix(y,LASSO_pre_class,positive = 'False.')## Confusion Matrix and Statistics
##
## Reference
## Prediction False. True.
## False. 2820 30
## True. 443 40
##
## Accuracy : 0.8581
## 95% CI : (0.8458, 0.8698)
## No Information Rate : 0.979
## P-Value [Acc > NIR] : 1
##
## Kappa : 0.1121
## Mcnemar's Test P-Value : <2e-16
##
## Sensitivity : 0.86424
## Specificity : 0.57143
## Pos Pred Value : 0.98947
## Neg Pred Value : 0.08282
## Prevalence : 0.97900
## Detection Rate : 0.84608
## Detection Prevalence : 0.85509
## Balanced Accuracy : 0.71783
##
## 'Positive' Class : False.
## 2. Receiver Operating Characteristic (ROC) Curve
Since the target variable is binary categorical, in addition to a confusion matrix, we can also evaluate the model with ROC curve.
preobs <- data.frame(prob=LASSO_pre, obs=churndata_1$Churn1)
head(preobs)## X1 obs
## 1 0.12861786 0
## 2 0.05963995 0
## 3 0.09574063 0
## 4 0.55501055 0
## 5 0.43729223 0
## 6 0.33011944 0modelroc = roc(preobs$obs, preobs$X1)
plot(modelroc, print.auc=TRUE, auc.polygon=T, grid=c(0.1,0.2),grid.col=c('green','red'),max.auc.polygon=TRUE, auc.polygon.col="skyblue", print.thres=TRUE)
##
## Call:
## roc.default(response = preobs$obs, predictor = preobs$X1)
##
## Data: preobs$X1 in 2850 controls (preobs$obs 0) < 483 cases (preobs$obs 1).
## Area under the curve: 0.8207ROC curve shows the tradeoff between sensitivity and specificity: The measure of sensitivity is the proportion of positive examples that were correctly classified. The measure of specificity is the proportion of negative examples that were correctly classified.
AUC: The area under the curve. It is equal to the probability that a classifier will rank a randomly chosen positive instance higher than a randomly chosen negative one.
Decision Tree Model
rpart() package is used to create the tree.
churndata_2 <- select(churndata_1,-Churn1)
Tree_model <- rpart(Churn.~., data = churndata_2)
summary(Tree_model)## Call:
## rpart(formula = Churn. ~ ., data = churndata_2)
## n= 3333
##
## CP nsplit rel error xerror xstd
## 1 0.08902692 0 1.0000000 1.0000000 0.04207569
## 2 0.08488613 1 0.9109731 0.9813665 0.04174759
## 3 0.07867495 2 0.8260870 0.8861284 0.03998804
## 4 0.05279503 4 0.6687371 0.6832298 0.03570013
## 5 0.01863354 7 0.4741201 0.4886128 0.03065927
## 6 0.01759834 8 0.4554865 0.4720497 0.03017404
## 7 0.01242236 13 0.3623188 0.4265010 0.02878278
## 8 0.01000000 16 0.3250518 0.4161491 0.02845405
##
## Variable importance
## Day.Charge Day.Mins CustServ.Calls Eve.Mins Eve.Charge
## 18 18 9 8 8
## Intl.Charge Intl.Mins Int.l.Plan Intl.Calls VMail.Message
## 8 8 6 5 5
## VMail.Plan Night.Calls Area.Code
## 5 1 1
##
## Node number 1: 3333 observations, complexity param=0.08902692
## predicted class=False. expected loss=0.1449145 P(node) =1
## class counts: 2850 483
## probabilities: 0.855 0.145
## left son=2 (3122 obs) right son=3 (211 obs)
## Primary splits:
## Day.Mins < 264.45 to the left, improve=94.083100, (0 missing)
## Day.Charge < 44.96 to the left, improve=94.083100, (0 missing)
## CustServ.Calls < 3.5 to the left, improve=80.306170, (0 missing)
## Int.l.Plan < 0.5 to the left, improve=55.774830, (0 missing)
## Intl.Mins < 13.15 to the left, improve= 8.656215, (0 missing)
## Surrogate splits:
## Day.Charge < 44.96 to the left, agree=1, adj=1, (0 split)
##
## Node number 2: 3122 observations, complexity param=0.07867495
## predicted class=False. expected loss=0.1140295 P(node) =0.9366937
## class counts: 2766 356
## probabilities: 0.886 0.114
## left son=4 (2871 obs) right son=5 (251 obs)
## Primary splits:
## CustServ.Calls < 3.5 to the left, improve=83.860470, (0 missing)
## Int.l.Plan < 0.5 to the left, improve=54.867830, (0 missing)
## Day.Mins < 223.25 to the left, improve=12.026250, (0 missing)
## Day.Charge < 37.95 to the left, improve=12.026250, (0 missing)
## Intl.Mins < 13.15 to the left, improve= 8.063614, (0 missing)
##
## Node number 3: 211 observations, complexity param=0.08488613
## predicted class=True. expected loss=0.3981043 P(node) =0.06330633
## class counts: 84 127
## probabilities: 0.398 0.602
## left son=6 (53 obs) right son=7 (158 obs)
## Primary splits:
## VMail.Plan < 0.5 to the right, improve=33.80609, (0 missing)
## VMail.Message < 6.5 to the right, improve=33.80609, (0 missing)
## Eve.Mins < 167.3 to the left, improve=14.73393, (0 missing)
## Eve.Charge < 14.22 to the left, improve=14.73393, (0 missing)
## Day.Mins < 316.7 to the left, improve= 7.00330, (0 missing)
## Surrogate splits:
## VMail.Message < 6.5 to the right, agree=1.000, adj=1.000, (0 split)
## Night.Calls < 50 to the left, agree=0.758, adj=0.038, (0 split)
## Account.Length < 15.5 to the left, agree=0.754, adj=0.019, (0 split)
##
## Node number 4: 2871 observations, complexity param=0.05279503
## predicted class=False. expected loss=0.07976315 P(node) =0.8613861
## class counts: 2642 229
## probabilities: 0.920 0.080
## left son=8 (2604 obs) right son=9 (267 obs)
## Primary splits:
## Int.l.Plan < 0.5 to the left, improve=52.464180, (0 missing)
## Day.Mins < 221.85 to the left, improve=19.883390, (0 missing)
## Day.Charge < 37.715 to the left, improve=19.883390, (0 missing)
## Intl.Mins < 13.15 to the left, improve= 8.200801, (0 missing)
## Intl.Charge < 3.55 to the left, improve= 8.200801, (0 missing)
##
## Node number 5: 251 observations, complexity param=0.07867495
## predicted class=True. expected loss=0.4940239 P(node) =0.07530753
## class counts: 124 127
## probabilities: 0.494 0.506
## left son=10 (149 obs) right son=11 (102 obs)
## Primary splits:
## Day.Mins < 160.2 to the right, improve=46.178350, (0 missing)
## Day.Charge < 27.235 to the right, improve=46.178350, (0 missing)
## Eve.Mins < 190.8 to the right, improve=11.171240, (0 missing)
## Eve.Charge < 16.22 to the right, improve=11.171240, (0 missing)
## CustServ.Calls < 4.5 to the left, improve= 4.362024, (0 missing)
## Surrogate splits:
## Day.Charge < 27.235 to the right, agree=1.000, adj=1.000, (0 split)
## Night.Calls < 79.5 to the right, agree=0.618, adj=0.059, (0 split)
## Area.Code < 462.5 to the left, agree=0.610, adj=0.039, (0 split)
## Eve.Mins < 118.6 to the right, agree=0.610, adj=0.039, (0 split)
## Eve.Charge < 10.08 to the right, agree=0.610, adj=0.039, (0 split)
##
## Node number 6: 53 observations
## predicted class=False. expected loss=0.1132075 P(node) =0.01590159
## class counts: 47 6
## probabilities: 0.887 0.113
##
## Node number 7: 158 observations, complexity param=0.01759834
## predicted class=True. expected loss=0.2341772 P(node) =0.04740474
## class counts: 37 121
## probabilities: 0.234 0.766
## left son=14 (57 obs) right son=15 (101 obs)
## Primary splits:
## Eve.Mins < 187.75 to the left, improve=19.095760, (0 missing)
## Eve.Charge < 15.96 to the left, improve=19.095760, (0 missing)
## Night.Mins < 206.85 to the left, improve= 4.867292, (0 missing)
## Night.Charge < 9.305 to the left, improve= 4.867292, (0 missing)
## Day.Mins < 278.45 to the left, improve= 4.754541, (0 missing)
## Surrogate splits:
## Eve.Charge < 15.96 to the left, agree=1.000, adj=1.000, (0 split)
## Intl.Mins < 3.35 to the left, agree=0.658, adj=0.053, (0 split)
## Intl.Charge < 0.905 to the left, agree=0.658, adj=0.053, (0 split)
## Account.Length < 20.5 to the left, agree=0.652, adj=0.035, (0 split)
## Day.Calls < 68 to the left, agree=0.652, adj=0.035, (0 split)
##
## Node number 8: 2604 observations, complexity param=0.01759834
## predicted class=False. expected loss=0.04915515 P(node) =0.7812781
## class counts: 2476 128
## probabilities: 0.951 0.049
## left son=16 (2221 obs) right son=17 (383 obs)
## Primary splits:
## Day.Mins < 223.25 to the left, improve=14.804280, (0 missing)
## Day.Charge < 37.95 to the left, improve=14.804280, (0 missing)
## Eve.Mins < 244.95 to the left, improve= 7.215623, (0 missing)
## Eve.Charge < 20.825 to the left, improve= 7.215623, (0 missing)
## Night.Mins < 163.85 to the left, improve= 1.727421, (0 missing)
## Surrogate splits:
## Day.Charge < 37.95 to the left, agree=1, adj=1, (0 split)
##
## Node number 9: 267 observations, complexity param=0.05279503
## predicted class=False. expected loss=0.3782772 P(node) =0.08010801
## class counts: 166 101
## probabilities: 0.622 0.378
## left son=18 (216 obs) right son=19 (51 obs)
## Primary splits:
## Intl.Calls < 2.5 to the right, improve=48.736160, (0 missing)
## Intl.Mins < 13.1 to the left, improve=45.240980, (0 missing)
## Intl.Charge < 3.535 to the left, improve=45.240980, (0 missing)
## Day.Mins < 220.05 to the left, improve= 2.335478, (0 missing)
## Day.Charge < 37.405 to the left, improve= 2.335478, (0 missing)
## Surrogate splits:
## Day.Calls < 48 to the right, agree=0.816, adj=0.039, (0 split)
## Night.Calls < 57.5 to the right, agree=0.813, adj=0.020, (0 split)
##
## Node number 10: 149 observations, complexity param=0.01863354
## predicted class=False. expected loss=0.2550336 P(node) =0.04470447
## class counts: 111 38
## probabilities: 0.745 0.255
## left son=20 (130 obs) right son=21 (19 obs)
## Primary splits:
## Eve.Mins < 141.75 to the right, improve=10.110570, (0 missing)
## Eve.Charge < 12.05 to the right, improve=10.110570, (0 missing)
## Day.Mins < 182.3 to the right, improve= 5.050074, (0 missing)
## Day.Charge < 30.995 to the right, improve= 5.050074, (0 missing)
## Night.Calls < 108 to the left, improve= 2.471396, (0 missing)
## Surrogate splits:
## Eve.Charge < 12.05 to the right, agree=1, adj=1, (0 split)
##
## Node number 11: 102 observations
## predicted class=True. expected loss=0.127451 P(node) =0.03060306
## class counts: 13 89
## probabilities: 0.127 0.873
##
## Node number 14: 57 observations, complexity param=0.01759834
## predicted class=False. expected loss=0.4385965 P(node) =0.01710171
## class counts: 32 25
## probabilities: 0.561 0.439
## left son=28 (25 obs) right son=29 (32 obs)
## Primary splits:
## Day.Mins < 277.7 to the left, improve=6.912675, (0 missing)
## Day.Charge < 47.21 to the left, improve=6.912675, (0 missing)
## Night.Mins < 212.65 to the left, improve=6.032297, (0 missing)
## Night.Charge < 9.57 to the left, improve=6.032297, (0 missing)
## Eve.Mins < 144.25 to the left, improve=5.632080, (0 missing)
## Surrogate splits:
## Day.Charge < 47.21 to the left, agree=1.000, adj=1.00, (0 split)
## Eve.Calls < 114 to the right, agree=0.684, adj=0.28, (0 split)
## Intl.Mins < 10.8 to the right, agree=0.649, adj=0.20, (0 split)
## Intl.Charge < 2.915 to the right, agree=0.649, adj=0.20, (0 split)
## Eve.Mins < 180.1 to the right, agree=0.632, adj=0.16, (0 split)
##
## Node number 15: 101 observations
## predicted class=True. expected loss=0.04950495 P(node) =0.03030303
## class counts: 5 96
## probabilities: 0.050 0.950
##
## Node number 16: 2221 observations
## predicted class=False. expected loss=0.02701486 P(node) =0.6663666
## class counts: 2161 60
## probabilities: 0.973 0.027
##
## Node number 17: 383 observations, complexity param=0.01759834
## predicted class=False. expected loss=0.1775457 P(node) =0.1149115
## class counts: 315 68
## probabilities: 0.822 0.178
## left son=34 (332 obs) right son=35 (51 obs)
## Primary splits:
## Eve.Mins < 259.8 to the left, improve=28.150970, (0 missing)
## Eve.Charge < 22.08 to the left, improve=28.150970, (0 missing)
## VMail.Plan < 0.5 to the right, improve= 6.313601, (0 missing)
## VMail.Message < 5.5 to the right, improve= 6.313601, (0 missing)
## Night.Mins < 181.15 to the left, improve= 4.818110, (0 missing)
## Surrogate splits:
## Eve.Charge < 22.08 to the left, agree=1.000, adj=1.00, (0 split)
## Intl.Mins < 2.05 to the right, agree=0.869, adj=0.02, (0 split)
## Intl.Charge < 0.555 to the right, agree=0.869, adj=0.02, (0 split)
##
## Node number 18: 216 observations, complexity param=0.05279503
## predicted class=False. expected loss=0.2314815 P(node) =0.06480648
## class counts: 166 50
## probabilities: 0.769 0.231
## left son=36 (173 obs) right son=37 (43 obs)
## Primary splits:
## Intl.Mins < 13.1 to the left, improve=63.418330, (0 missing)
## Intl.Charge < 3.535 to the left, improve=63.418330, (0 missing)
## Eve.Mins < 163.4 to the left, improve= 2.123757, (0 missing)
## Eve.Charge < 13.885 to the left, improve= 2.123757, (0 missing)
## Day.Mins < 237.2 to the left, improve= 1.910053, (0 missing)
## Surrogate splits:
## Intl.Charge < 3.535 to the left, agree=1.000, adj=1.000, (0 split)
## VMail.Message < 40.5 to the left, agree=0.806, adj=0.023, (0 split)
## Day.Mins < 52.45 to the right, agree=0.806, adj=0.023, (0 split)
## Day.Charge < 8.92 to the right, agree=0.806, adj=0.023, (0 split)
## Night.Calls < 141.5 to the left, agree=0.806, adj=0.023, (0 split)
##
## Node number 19: 51 observations
## predicted class=True. expected loss=0 P(node) =0.01530153
## class counts: 0 51
## probabilities: 0.000 1.000
##
## Node number 20: 130 observations, complexity param=0.01242236
## predicted class=False. expected loss=0.1846154 P(node) =0.0390039
## class counts: 106 24
## probabilities: 0.815 0.185
## left son=40 (96 obs) right son=41 (34 obs)
## Primary splits:
## Day.Mins < 175.75 to the right, improve=4.751207, (0 missing)
## Day.Charge < 29.88 to the right, improve=4.751207, (0 missing)
## Night.Calls < 108 to the left, improve=2.946628, (0 missing)
## Day.Calls < 131 to the left, improve=2.213955, (0 missing)
## Intl.Mins < 13.7 to the left, improve=1.743620, (0 missing)
## Surrogate splits:
## Day.Charge < 29.88 to the right, agree=1.000, adj=1.000, (0 split)
## Day.Calls < 143 to the left, agree=0.754, adj=0.059, (0 split)
## Intl.Mins < 4.85 to the right, agree=0.746, adj=0.029, (0 split)
## Intl.Charge < 1.31 to the right, agree=0.746, adj=0.029, (0 split)
##
## Node number 21: 19 observations
## predicted class=True. expected loss=0.2631579 P(node) =0.00570057
## class counts: 5 14
## probabilities: 0.263 0.737
##
## Node number 28: 25 observations
## predicted class=False. expected loss=0.16 P(node) =0.00750075
## class counts: 21 4
## probabilities: 0.840 0.160
##
## Node number 29: 32 observations, complexity param=0.01242236
## predicted class=True. expected loss=0.34375 P(node) =0.00960096
## class counts: 11 21
## probabilities: 0.344 0.656
## left son=58 (8 obs) right son=59 (24 obs)
## Primary splits:
## Eve.Mins < 144.35 to the left, improve=6.020833, (0 missing)
## Eve.Charge < 12.27 to the left, improve=6.020833, (0 missing)
## Intl.Calls < 4.5 to the right, improve=3.708088, (0 missing)
## Night.Mins < 210.35 to the left, improve=3.691468, (0 missing)
## Night.Charge < 9.465 to the left, improve=3.691468, (0 missing)
## Surrogate splits:
## Eve.Charge < 12.27 to the left, agree=1.000, adj=1.00, (0 split)
## Intl.Mins < 7.25 to the left, agree=0.812, adj=0.25, (0 split)
## Intl.Charge < 1.955 to the left, agree=0.812, adj=0.25, (0 split)
##
## Node number 34: 332 observations
## predicted class=False. expected loss=0.1024096 P(node) =0.09960996
## class counts: 298 34
## probabilities: 0.898 0.102
##
## Node number 35: 51 observations, complexity param=0.01759834
## predicted class=True. expected loss=0.3333333 P(node) =0.01530153
## class counts: 17 34
## probabilities: 0.333 0.667
## left son=70 (11 obs) right son=71 (40 obs)
## Primary splits:
## VMail.Plan < 0.5 to the right, improve=12.466670, (0 missing)
## VMail.Message < 5.5 to the right, improve=12.466670, (0 missing)
## Night.Mins < 256.15 to the right, improve= 2.354978, (0 missing)
## Night.Charge < 11.525 to the right, improve= 2.354978, (0 missing)
## Night.Calls < 113 to the left, improve= 2.294197, (0 missing)
## Surrogate splits:
## VMail.Message < 5.5 to the right, agree=1.000, adj=1.000, (0 split)
## Night.Mins < 256.15 to the right, agree=0.843, adj=0.273, (0 split)
## Night.Charge < 11.525 to the right, agree=0.843, adj=0.273, (0 split)
## Eve.Calls < 68 to the left, agree=0.804, adj=0.091, (0 split)
##
## Node number 36: 173 observations
## predicted class=False. expected loss=0.04046243 P(node) =0.05190519
## class counts: 166 7
## probabilities: 0.960 0.040
##
## Node number 37: 43 observations
## predicted class=True. expected loss=0 P(node) =0.01290129
## class counts: 0 43
## probabilities: 0.000 1.000
##
## Node number 40: 96 observations
## predicted class=False. expected loss=0.1041667 P(node) =0.02880288
## class counts: 86 10
## probabilities: 0.896 0.104
##
## Node number 41: 34 observations, complexity param=0.01242236
## predicted class=False. expected loss=0.4117647 P(node) =0.01020102
## class counts: 20 14
## probabilities: 0.588 0.412
## left son=82 (18 obs) right son=83 (16 obs)
## Primary splits:
## Eve.Mins < 212.15 to the right, improve=12.970590, (0 missing)
## Eve.Charge < 18.03 to the right, improve=12.970590, (0 missing)
## Night.Calls < 101.5 to the left, improve= 3.488132, (0 missing)
## Area.Code < 411.5 to the left, improve= 2.800259, (0 missing)
## Night.Mins < 172.9 to the right, improve= 1.213445, (0 missing)
## Surrogate splits:
## Eve.Charge < 18.03 to the right, agree=1.000, adj=1.000, (0 split)
## Night.Calls < 97 to the left, agree=0.765, adj=0.500, (0 split)
## Area.Code < 411.5 to the left, agree=0.676, adj=0.313, (0 split)
## Intl.Mins < 14.3 to the left, agree=0.647, adj=0.250, (0 split)
## Intl.Charge < 3.865 to the left, agree=0.647, adj=0.250, (0 split)
##
## Node number 58: 8 observations
## predicted class=False. expected loss=0.125 P(node) =0.00240024
## class counts: 7 1
## probabilities: 0.875 0.125
##
## Node number 59: 24 observations
## predicted class=True. expected loss=0.1666667 P(node) =0.00720072
## class counts: 4 20
## probabilities: 0.167 0.833
##
## Node number 70: 11 observations
## predicted class=False. expected loss=0 P(node) =0.00330033
## class counts: 11 0
## probabilities: 1.000 0.000
##
## Node number 71: 40 observations
## predicted class=True. expected loss=0.15 P(node) =0.0120012
## class counts: 6 34
## probabilities: 0.150 0.850
##
## Node number 82: 18 observations
## predicted class=False. expected loss=0 P(node) =0.00540054
## class counts: 18 0
## probabilities: 1.000 0.000
##
## Node number 83: 16 observations
## predicted class=True. expected loss=0.125 P(node) =0.00480048
## class counts: 2 14
## probabilities: 0.125 0.875Visualization of the Tree Model
fancyRpartPlot(Tree_model)
Validation of Decision Tree
To validate the model we use the printcp and plotcp functions. ‘CP’ stands for Complexity Parameter of the tree.
printcp() provides the optimal prunings based on the cp value. We prune the tree to avoid any overfitting of the data. The convention is to have a small tree and the one with least cross validated error given by printcp() function i.e. ‘xerror’.
printcp(Tree_model)##
## Classification tree:
## rpart(formula = Churn. ~ ., data = churndata_2)
##
## Variables actually used in tree construction:
## [1] CustServ.Calls Day.Mins Eve.Mins Int.l.Plan
## [5] Intl.Calls Intl.Mins VMail.Plan
##
## Root node error: 483/3333 = 0.14491
##
## n= 3333
##
## CP nsplit rel error xerror xstd
## 1 0.089027 0 1.00000 1.00000 0.042076
## 2 0.084886 1 0.91097 0.98137 0.041748
## 3 0.078675 2 0.82609 0.88613 0.039988
## 4 0.052795 4 0.66874 0.68323 0.035700
## 5 0.018634 7 0.47412 0.48861 0.030659
## 6 0.017598 8 0.45549 0.47205 0.030174
## 7 0.012422 13 0.36232 0.42650 0.028783
## 8 0.010000 16 0.32505 0.41615 0.028454Select the optimal cp value associated with the minimum error:
Tree_model$cptable[which.min(Tree_model$cptable[,"xerror"]),"CP"]## [1] 0.01Plotcp() provides a graphical representation to the cross validated error summary:
plotcp(Tree_model)
According to teh printcp and plotcp result, the original tree with all 17 factors is the optimal decision without overfitting. There is no need to prune the tree.
Prediction
Tree_pre <- predict(Tree_model, type = 'class')
Tree_pre2 <- predict(Tree_model, type = 'prob')Model Evalution
1. ConfusionMatrix
table(churndata_2$Churn.,Tree_pre)## Tree_pre
## False. True.
## False. 2815 35
## True. 122 361confusionMatrix(churndata_2$Churn.,Tree_pre,positive = 'False.')## Confusion Matrix and Statistics
##
## Reference
## Prediction False. True.
## False. 2815 35
## True. 122 361
##
## Accuracy : 0.9529
## 95% CI : (0.9451, 0.9598)
## No Information Rate : 0.8812
## P-Value [Acc > NIR] : < 2.2e-16
##
## Kappa : 0.7946
## Mcnemar's Test P-Value : 6.717e-12
##
## Sensitivity : 0.9585
## Specificity : 0.9116
## Pos Pred Value : 0.9877
## Neg Pred Value : 0.7474
## Prevalence : 0.8812
## Detection Rate : 0.8446
## Detection Prevalence : 0.8551
## Balanced Accuracy : 0.9350
##
## 'Positive' Class : False.
## 2. Receiver Operating Characteristic (ROC) Curve
preobs2 <- data.frame(prob=Tree_pre2[,1], obs=churndata_1$Churn1)
head(preobs2)## prob obs
## 1 0.8867925 0
## 2 0.9729851 0
## 3 0.8975904 0
## 4 0.8750000 0
## 5 0.9595376 0
## 6 0.9595376 0modelroc2 = roc(preobs2$obs, preobs2$prob)
plot(modelroc2, print.auc=TRUE, auc.polygon=T, grid=c(0.1,0.2),grid.col=c('green','red'),max.auc.polygon=TRUE, auc.polygon.col="skyblue", print.thres=TRUE)
##
## Call:
## roc.default(response = preobs2$obs, predictor = preobs2$prob)
##
## Data: preobs2$prob in 2850 controls (preobs2$obs 0) > 483 cases (preobs2$obs 1).
## Area under the curve: 0.9086Conclusion
By comparing the AUC value (0.820 vs. 0.909), and the criteria in ConfusionMatrix, the Decision Tree Model performs better than Logistic Regression, it has been selected for further prediction.
The code could be download from my github: churn_analysis.R