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Predict Customer Churn – Logistic Regression, Decision Tree and Random Forest

• Published on November 20, 2017 at 9:00 am

Customer churn occurs when customers or subscribers stop doing business with a company or service, also known as customer attrition. It is also referred as loss of clients or customers. One industry in which churn rates are particularly useful is the telecommunications industry, because most customers have multiple options from which to choose within a geographic location.

Similar concept with predicting employee turnover, we are going to predict customer churn using telecom dataset. We will introduce Logistic Regression, Decision Tree, and Random Forest. But this time, we will do all of the above in R. Let’s get started!

Data Preprocessing

The data was downloaded from IBM Sample Data Sets. Each row represents a customer, each column contains that customer’s attributes:

library(plyr)
library(corrplot)
library(ggplot2)
library(gridExtra)
library(ggthemes)
library(caret)
library(MASS)
library(randomForest)
library(party)

str(churn)
'data.frame':	7043 obs. of  21 variables:
$customerID : Factor w/ 7043 levels "0002-ORFBO","0003-MKNFE",..: 5376 3963 2565 5536 6512 6552 1003 4771 5605 4535 ...$ gender          : Factor w/ 2 levels "Female","Male": 1 2 2 2 1 1 2 1 1 2 ...
$SeniorCitizen : int 0 0 0 0 0 0 0 0 0 0 ...$ Partner         : Factor w/ 2 levels "No","Yes": 2 1 1 1 1 1 1 1 2 1 ...
$Dependents : Factor w/ 2 levels "No","Yes": 1 1 1 1 1 1 2 1 1 2 ...$ tenure          : int  1 34 2 45 2 8 22 10 28 62 ...
$PhoneService : Factor w/ 2 levels "No","Yes": 1 2 2 1 2 2 2 1 2 2 ...$ MultipleLines   : Factor w/ 3 levels "No","No phone service",..: 2 1 1 2 1 3 3 2 3 1 ...
$InternetService : Factor w/ 3 levels "DSL","Fiber optic",..: 1 1 1 1 2 2 2 1 2 1 ...$ OnlineSecurity  : Factor w/ 3 levels "No","No internet service",..: 1 3 3 3 1 1 1 3 1 3 ...
$OnlineBackup : Factor w/ 3 levels "No","No internet service",..: 3 1 3 1 1 1 3 1 1 3 ...$ DeviceProtection: Factor w/ 3 levels "No","No internet service",..: 1 3 1 3 1 3 1 1 3 1 ...
$TechSupport : Factor w/ 3 levels "No","No internet service",..: 1 1 1 3 1 1 1 1 3 1 ...$ StreamingTV     : Factor w/ 3 levels "No","No internet service",..: 1 1 1 1 1 3 3 1 3 1 ...
$StreamingMovies : Factor w/ 3 levels "No","No internet service",..: 1 1 1 1 1 3 1 1 3 1 ...$ Contract        : Factor w/ 3 levels "Month-to-month",..: 1 2 1 2 1 1 1 1 1 2 ...
$PaperlessBilling: Factor w/ 2 levels "No","Yes": 2 1 2 1 2 2 2 1 2 1 ...$ PaymentMethod   : Factor w/ 4 levels "Bank transfer (automatic)",..: 3 4 4 1 3 3 2 4 3 1 ...
$MonthlyCharges : num 29.9 57 53.9 42.3 70.7 ...$ TotalCharges    : num  29.9 1889.5 108.2 1840.8 151.7 ...
churn$tenure <- NULL  Exploratory data analysis and feature selection Correlation between numeric variables numeric.var <- sapply(churn, is.numeric) corr.matrix <- cor(churn[,numeric.var]) corrplot(corr.matrix, main="\n\nCorrelation Plot for Numerical Variables", method="number")  Gives this plot: The Monthly Charges and Total Charges are correlated. So one of them will be removed from the model. We remove Total Charges. churn$TotalCharges <- NULL


Bar plots of categorical variables

p1 <- ggplot(churn, aes(x=gender)) + ggtitle("Gender") + xlab("Gender") +
geom_bar(aes(y = 100*(..count..)/sum(..count..)), width = 0.5) + ylab("Percentage") + coord_flip() + theme_minimal()
p2 <- ggplot(churn, aes(x=SeniorCitizen)) + ggtitle("Senior Citizen") + xlab("Senior Citizen") +
geom_bar(aes(y = 100*(..count..)/sum(..count..)), width = 0.5) + ylab("Percentage") + coord_flip() + theme_minimal()
p3 <- ggplot(churn, aes(x=Partner)) + ggtitle("Partner") + xlab("Partner") +
geom_bar(aes(y = 100*(..count..)/sum(..count..)), width = 0.5) + ylab("Percentage") + coord_flip() + theme_minimal()
p4 <- ggplot(churn, aes(x=Dependents)) + ggtitle("Dependents") + xlab("Dependents") +
geom_bar(aes(y = 100*(..count..)/sum(..count..)), width = 0.5) + ylab("Percentage") + coord_flip() + theme_minimal()
grid.arrange(p1, p2, p3, p4, ncol=2)


Gives this plot:

p5 <- ggplot(churn, aes(x=PhoneService)) + ggtitle("Phone Service") + xlab("Phone Service") +
geom_bar(aes(y = 100*(..count..)/sum(..count..)), width = 0.5) + ylab("Percentage") + coord_flip() + theme_minimal()
p6 <- ggplot(churn, aes(x=MultipleLines)) + ggtitle("Multiple Lines") + xlab("Multiple Lines") +
geom_bar(aes(y = 100*(..count..)/sum(..count..)), width = 0.5) + ylab("Percentage") + coord_flip() + theme_minimal()
p7 <- ggplot(churn, aes(x=InternetService)) + ggtitle("Internet Service") + xlab("Internet Service") +
geom_bar(aes(y = 100*(..count..)/sum(..count..)), width = 0.5) + ylab("Percentage") + coord_flip() + theme_minimal()
p8 <- ggplot(churn, aes(x=OnlineSecurity)) + ggtitle("Online Security") + xlab("Online Security") +
geom_bar(aes(y = 100*(..count..)/sum(..count..)), width = 0.5) + ylab("Percentage") + coord_flip() + theme_minimal()
grid.arrange(p5, p6, p7, p8, ncol=2)


Gives this plot:

p9 <- ggplot(churn, aes(x=OnlineBackup)) + ggtitle("Online Backup") + xlab("Online Backup") +
geom_bar(aes(y = 100*(..count..)/sum(..count..)), width = 0.5) + ylab("Percentage") + coord_flip() + theme_minimal()
p10 <- ggplot(churn, aes(x=DeviceProtection)) + ggtitle("Device Protection") + xlab("Device Protection") +
geom_bar(aes(y = 100*(..count..)/sum(..count..)), width = 0.5) + ylab("Percentage") + coord_flip() + theme_minimal()
p11 <- ggplot(churn, aes(x=TechSupport)) + ggtitle("Tech Support") + xlab("Tech Support") +
geom_bar(aes(y = 100*(..count..)/sum(..count..)), width = 0.5) + ylab("Percentage") + coord_flip() + theme_minimal()
p12 <- ggplot(churn, aes(x=StreamingTV)) + ggtitle("Streaming TV") + xlab("Streaming TV") +
geom_bar(aes(y = 100*(..count..)/sum(..count..)), width = 0.5) + ylab("Percentage") + coord_flip() + theme_minimal()
grid.arrange(p9, p10, p11, p12, ncol=2)


Gives this plot:

p13 <- ggplot(churn, aes(x=StreamingMovies)) + ggtitle("Streaming Movies") + xlab("Streaming Movies") +
geom_bar(aes(y = 100*(..count..)/sum(..count..)), width = 0.5) + ylab("Percentage") + coord_flip() + theme_minimal()
p14 <- ggplot(churn, aes(x=Contract)) + ggtitle("Contract") + xlab("Contract") +
geom_bar(aes(y = 100*(..count..)/sum(..count..)), width = 0.5) + ylab("Percentage") + coord_flip() + theme_minimal()
p15 <- ggplot(churn, aes(x=PaperlessBilling)) + ggtitle("Paperless Billing") + xlab("Paperless Billing") +
geom_bar(aes(y = 100*(..count..)/sum(..count..)), width = 0.5) + ylab("Percentage") + coord_flip() + theme_minimal()
p16 <- ggplot(churn, aes(x=PaymentMethod)) + ggtitle("Payment Method") + xlab("Payment Method") +
geom_bar(aes(y = 100*(..count..)/sum(..count..)), width = 0.5) + ylab("Percentage") + coord_flip() + theme_minimal()
p17 <- ggplot(churn, aes(x=tenure_group)) + ggtitle("Tenure Group") + xlab("Tenure Group") +
geom_bar(aes(y = 100*(..count..)/sum(..count..)), width = 0.5) + ylab("Percentage") + coord_flip() + theme_minimal()
grid.arrange(p13, p14, p15, p16, p17, ncol=2)


Gives this plot:

All of the categorical variables seem to have a reasonably broad distribution, therefore, all of them will be kept for the further analysis.

Logistic Regression

First, we split the data into training and testing sets

intrain<- createDataPartition(churn$Churn,p=0.7,list=FALSE) set.seed(2017) training<- churn[intrain,] testing<- churn[-intrain,]  Confirm the splitting is correct dim(training); dim(testing) [1] 4924 19 [1] 2108 19  Fitting the Logistic Regression Model LogModel <- glm(Churn ~ .,family=binomial(link="logit"),data=training) print(summary(LogModel)) Call: glm(formula = Churn ~ ., family = binomial(link = "logit"), data = training) Deviance Residuals: Min 1Q Median 3Q Max -2.0370 -0.6793 -0.2861 0.6590 3.1608 Coefficients: Estimate Std. Error z value Pr(>|z|) (Intercept) -2.030149 1.008223 -2.014 0.044053 * genderMale -0.039006 0.077686 -0.502 0.615603 SeniorCitizenYes 0.194408 0.101151 1.922 0.054611 . PartnerYes -0.062031 0.092911 -0.668 0.504363 DependentsYes -0.017974 0.107659 -0.167 0.867405 PhoneServiceYes -0.387097 0.788745 -0.491 0.623585 MultipleLinesYes 0.345052 0.214799 1.606 0.108187 InternetServiceFiber optic 1.022836 0.968062 1.057 0.290703 InternetServiceNo -0.829521 0.978909 -0.847 0.396776 OnlineSecurityYes -0.393647 0.215993 -1.823 0.068379 . OnlineBackupYes -0.113220 0.213825 -0.529 0.596460 DeviceProtectionYes -0.025797 0.213317 -0.121 0.903744 TechSupportYes -0.306423 0.220920 -1.387 0.165433 StreamingTVYes 0.399209 0.395912 1.008 0.313297 StreamingMoviesYes 0.338852 0.395890 0.856 0.392040 ContractOne year -0.805584 0.127125 -6.337 2.34e-10 *** ContractTwo year -1.662793 0.216346 -7.686 1.52e-14 *** PaperlessBillingYes 0.338724 0.089407 3.789 0.000152 *** PaymentMethodCredit card (automatic) -0.018574 0.135318 -0.137 0.890826 PaymentMethodElectronic check 0.373214 0.113029 3.302 0.000960 *** PaymentMethodMailed check 0.001400 0.136446 0.010 0.991815 MonthlyCharges -0.005001 0.038558 -0.130 0.896797 tenure_group0-12 Month 1.858899 0.205956 9.026 < 2e-16 *** tenure_group12-24 Month 0.968497 0.201452 4.808 1.53e-06 *** tenure_group24-48 Month 0.574822 0.185500 3.099 0.001943 ** tenure_group48-60 Month 0.311790 0.200096 1.558 0.119185 --- Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 (Dispersion parameter for binomial family taken to be 1) Null deviance: 5702.8 on 4923 degrees of freedom Residual deviance: 4094.4 on 4898 degrees of freedom AIC: 4146.4 Number of Fisher Scoring iterations: 6  Feature Analysis The top three most-relevant features include Contract, tenure_group and PaperlessBilling. anova(LogModel, test="Chisq") Analysis of Deviance Table Model: binomial, link: logit Response: Churn Terms added sequentially (first to last) Df Deviance Resid. Df Resid. Dev Pr(>Chi) NULL 4923 5702.8 gender 1 0.39 4922 5702.4 0.5318602 SeniorCitizen 1 95.08 4921 5607.3 < 2.2e-16 *** Partner 1 107.29 4920 5500.0 < 2.2e-16 *** Dependents 1 27.26 4919 5472.7 1.775e-07 *** PhoneService 1 1.27 4918 5471.5 0.2597501 MultipleLines 1 9.63 4917 5461.8 0.0019177 ** InternetService 2 452.01 4915 5009.8 < 2.2e-16 *** OnlineSecurity 1 183.83 4914 4826.0 < 2.2e-16 *** OnlineBackup 1 69.94 4913 4756.1 < 2.2e-16 *** DeviceProtection 1 47.58 4912 4708.5 5.287e-12 *** TechSupport 1 82.78 4911 4625.7 < 2.2e-16 *** StreamingTV 1 4.90 4910 4620.8 0.0269174 * StreamingMovies 1 0.36 4909 4620.4 0.5461056 Contract 2 309.25 4907 4311.2 < 2.2e-16 *** PaperlessBilling 1 14.21 4906 4297.0 0.0001638 *** PaymentMethod 3 38.85 4903 4258.1 1.867e-08 *** MonthlyCharges 1 0.10 4902 4258.0 0.7491553 tenure_group 4 163.67 4898 4094.4 < 2.2e-16 *** --- Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1  Analyzing the deviance table we can see the drop in deviance when adding each variable one at a time. Adding InternetService, Contract and tenure_group significantly reduces the residual deviance. The other variables such as PaymentMethod and Dependents seem to improve the model less even though they all have low p-values. Assessing the predictive ability of the Logistic Regression model testing$Churn <- as.character(testing$Churn) testing$Churn[testing$Churn=="No"] <- "0" testing$Churn[testing$Churn=="Yes"] <- "1" fitted.results <- predict(LogModel,newdata=testing,type='response') fitted.results 0.5,1,0) misClasificError <- mean(fitted.results != testing$Churn)
print(paste('Logistic Regression Accuracy',1-misClasificError))
[1] "Logistic Regression Accuracy 0.796489563567362"



Logistic Regression Confusion Matrix

print("Confusion Matrix for Logistic Regression"); table(testing$Churn, fitted.results > 0.5) [1] "Confusion Matrix for Logistic Regression" FALSE TRUE 0 1392 156 1 273 287  Odds Ratio One of the interesting performance measurements in logistic regression is Odds Ratio.Basically, Odds ratio is what the odds of an event is happening. exp(cbind(OR=coef(LogModel), confint(LogModel))) Waiting for profiling to be done... OR 2.5 % 97.5 % (Intercept) 0.1313160 0.01815817 0.9461855 genderMale 0.9617454 0.82587632 1.1199399 SeniorCitizenYes 1.2145919 0.99591418 1.4807053 PartnerYes 0.9398537 0.78338071 1.1276774 DependentsYes 0.9821863 0.79488224 1.2124072 PhoneServiceYes 0.6790251 0.14466019 3.1878587 MultipleLinesYes 1.4120635 0.92707245 2.1522692 InternetServiceFiber optic 2.7810695 0.41762316 18.5910286 InternetServiceNo 0.4362582 0.06397364 2.9715699 OnlineSecurityYes 0.6745919 0.44144273 1.0296515 OnlineBackupYes 0.8929545 0.58709919 1.3577947 DeviceProtectionYes 0.9745328 0.64144877 1.4805460 TechSupportYes 0.7360754 0.47707096 1.1344691 StreamingTVYes 1.4906458 0.68637788 3.2416264 StreamingMoviesYes 1.4033353 0.64624171 3.0518161 ContractOne year 0.4468271 0.34725066 0.5717469 ContractTwo year 0.1896086 0.12230199 0.2861341 PaperlessBillingYes 1.4031556 1.17798691 1.6725920 PaymentMethodCredit card (automatic) 0.9815977 0.75273387 1.2797506 PaymentMethodElectronic check 1.4523952 1.16480721 1.8145076 PaymentMethodMailed check 1.0014007 0.76673087 1.3092444 MonthlyCharges 0.9950112 0.92252949 1.0731016 tenure_group0-12 Month 6.4166692 4.30371945 9.6544837 tenure_group12-24 Month 2.6339823 1.78095906 3.9256133 tenure_group24-48 Month 1.7768147 1.23988035 2.5676783 tenure_group48-60 Month 1.3658675 0.92383315 2.0261505  Decision Tree Decision Tree visualization For illustration purpose, we are going to use only three variables for plotting Decision Trees, they are “Contract”, “tenure_group” and “PaperlessBilling”. tree <- ctree(Churn~Contract+tenure_group+PaperlessBilling, training) plot(tree, type='simple')  Gives this plot: 1. Out of three variables we use, Contract is the most important variable to predict customer churn or not churn. 2. If a customer in a one-year or two-year contract, no matter he (she) has PapelessBilling or not, he (she) is less likely to churn. 3. On the other hand, if a customer is in a month-to-month contract, and in the tenure group of 0–12 month, and using PaperlessBilling, then this customer is more likely to churn. Decision Tree Confusion Matrix We are using all the variables to product confusion matrix table and make predictions. pred_tree <- predict(tree, testing) print("Confusion Matrix for Decision Tree"); table(Predicted = pred_tree, Actual = testing$Churn)
[1] "Confusion Matrix for Decision Tree"
Actual
Predicted   No  Yes
No  1395  346
Yes  153  214



Decision Tree Accuracy

p1 <- predict(tree, training)
tab1 <- table(Predicted = p1, Actual = training$Churn) tab2 <- table(Predicted = pred_tree, Actual = testing$Churn)
print(paste('Decision Tree Accuracy',sum(diag(tab2))/sum(tab2)))
[1] "Decision Tree Accuracy 0.763282732447818"



The accuracy for Decision Tree has hardly improved. Let’s see if we can do better using Random Forest.

Random Forest

Random Forest Initial Model

rfModel <- randomForest(Churn ~., data = training)
print(rfModel)
Call:
randomForest(formula = Churn ~ ., data = training)
Type of random forest: classification
Number of trees: 500
No. of variables tried at each split: 4

OOB estimate of  error rate: 20.65%
Confusion matrix:
No Yes class.error
No  3245 370   0.1023513
Yes  647 662   0.4942704



The error rate is relatively low when predicting “No”, and the error rate is much higher when predicting “Yes”.

Random Forest Prediction and Confusion Matrix

pred_rf <- predict(rfModel, testing)
caret::confusionMatrix(pred_rf, testing$Churn) Confusion Matrix and Statistics Reference Prediction No Yes No 1381 281 Yes 167 279 Accuracy : 0.7875 95% CI : (0.7694, 0.8048) No Information Rate : 0.7343 P-Value [Acc > NIR] : 9.284e-09 Kappa : 0.4175 Mcnemar's Test P-Value : 9.359e-08 Sensitivity : 0.8921 Specificity : 0.4982 Pos Pred Value : 0.8309 Neg Pred Value : 0.6256 Prevalence : 0.7343 Detection Rate : 0.6551 Detection Prevalence : 0.7884 Balanced Accuracy : 0.6952 'Positive' Class : No  Random Forest Error Rate plot(rfModel)  Gives this plot: We use this plot to help us determine the number of trees. As the number of trees increases, the OOB error rate decreases, and then becomes almost constant. We are not able to decrease the OOB error rate after about 100 to 200 trees. Tune Random Forest Model t <- tuneRF(training[, -18], training[, 18], stepFactor = 0.5, plot = TRUE, ntreeTry = 200, trace = TRUE, improve = 0.05)  Gives this plot: We use this plot to give us some ideas on the number of mtry to choose. OOB error rate is at the lowest when mtry is 2. Therefore, we choose mtry=2. Fit the Random Forest Model After Tuning rfModel_new <- randomForest(Churn ~., data = training, ntree = 200, mtry = 2, importance = TRUE, proximity = TRUE) print(rfModel_new) Call: randomForest(formula = Churn ~ ., data = training, ntree = 200, mtry = 2, importance = TRUE, proximity = TRUE) Type of random forest: classification Number of trees: 200 No. of variables tried at each split: 2 OOB estimate of error rate: 19.7% Confusion matrix: No Yes class.error No 3301 314 0.0868603 Yes 656 653 0.5011459  OOB error rate decreased to 19.7% from 20.65% earlier. Random Forest Predictions and Confusion Matrix After Tuning pred_rf_new <- predict(rfModel_new, testing) caret::confusionMatrix(pred_rf_new, testing$Churn)
Confusion Matrix and Statistics

Reference
Prediction   No  Yes
No  1404  305
Yes  144  255

Accuracy : 0.787
95% CI : (0.7689, 0.8043)
No Information Rate : 0.7343
P-Value [Acc > NIR] : 1.252e-08

Kappa : 0.3989
Mcnemar's Test P-Value : 4.324e-14

Sensitivity : 0.9070
Specificity : 0.4554
Pos Pred Value : 0.8215
Neg Pred Value : 0.6391
Prevalence : 0.7343
Detection Rate : 0.6660
Detection Prevalence : 0.8107
Balanced Accuracy : 0.6812

'Positive' Class : No



The accuracy did not increase but the sensitivity improved, compare with the initial Random Forest model.

Random Forest Feature Importance

varImpPlot(rfModel_new, sort=T, n.var = 10, main = 'Top 10 Feature Importance')


Gives this plot:

Summary

From the above example, we can see that Logistic Regression and Random Forest performed better than Decision Tree for customer churn analysis for this particular dataset.

Throughout the analysis, I have learned several important things:
1. Features such as tenure_group, Contract, PaperlessBilling, MonthlyCharges and InternetService appear to play a role in customer churn.
2. There does not seem to be a relationship between gender and churn.
3. Customers in a month-to-month contract, with PaperlessBilling and are within 12 months tenure, are more likely to churn; On the other hand, customers with one or two year contract, with longer than 12 months tenure, that are not using PaperlessBilling, are less likely to churn.

Source code that created this post can be found here. I would be pleased to receive feedback or questions on any of the above.