Predicting Customer Churn at Telco
Background
Telco is a hypothetical telecommunications company. Like any company that offers contract / subscription based services customers canceling services is an ongoing problem.
Services they provide include:
- Phone Service
- Internet Service
- Online Security
- Online Backup
- Streaming TV
- Streaming Movies
They have asked me to build a model to predict customer churn so that at risk customers can be identified and given special offers so that they stay with the company.
The data used is from Kaggle. There are 7,043 customers.
A churn is a customer who left within the last month.
The three classification models I built predict, but also provide information about factors driving churn.
- Regularized Logistic Regression (Lasso)
- Random Forest
- Gradient Bossting
Some key features from in the influencing churn at Telco are:
- Contract Type
- Customer Tenure in Months
- Online Security
- Monthly Charges
- Tech Support
You will see later on in my exploratory data analysis why these features are important.
First I am going to walk you through the process that I went through to build the model for this company.
70% of the customers was used to train the models and 30% was used for testing.
Exploratory Data Analysis
Missing values
There were not any missing values in the data.
Outliers in the data
There are only three numeric features in the data and there were not any outliers. The boxplots below confirm that.
Relationship of numeric features with Churn in the training data.
The numeric factors were broken out into deciles for analysis.
A decile is comprised of ten percentiles. For example, if a student's test score is in the 90th percentile, it means that he/she scored in the top 10 percent. It would be equivalent to say that his/her score is in the tenth decile as that also means the top 10 percent.
As the value of a numeric factor increases the range of values in each decile increases.
The churn rate within each decile was calculated and indexed to the overall churn rate of 27% using the following calculations:
Overall Churn Rate = (Number Of Churns) / (Total Number Of Customers)
Index = (Churn Rate Within Each Decile) / Overall Churn Rate) * 100
Customer Tenure has a strong negative relationship with churn. Newer customers are much more likely to churn. I've built a number of logistic regression models in the course of my career and Customer Tenure has always been the strongest feature in the model. It was the strongest feature in the logistic regression model for this project as well.
Monthly Charges have a positive relationship with churn.
Total Charges have a negative relationship with churn. Most likely because customers with longer tenure have paid more than newer ones. The correlation between Customer Tenure and Total Charges is 0.83.
Relationship of key categorical features with Churn in the training data.
For the categorical factors, each category was indexed to the overall churn rate of 27% using the following calculation:
Index = (Churn Rate Per Category) / (Overall Churn Rate) * 100
Note: when the index of the Churn Rate Per Category is equivalent to the Overall Churn Rate the index = 100
Customers with month-to-month contracts are more likely to churn with an index of 161 and a churn rate of 43%. 55% of customers fall into this category.
Customers who do not have online security are much more likely to churn with and index of 158 and a churn rate of 42%. 49% of customers fall into this category.
Customers without tech support are more likely to churn. 50% of customers fall into this category.
Models
As previously mentioned, three different models were built:
One Linear Model
- Regularized Logistic Regression (Lasso).
Two Tree Based Models:
- Random Forest
- Gradient Boosting
For all three models the AUC ROC was used for grid search.
Regularized Logistic Regression (Lasso)
I examined the numeric features for multicollinearity.
Tenure and Total Charges have variance inflation factors greater than five. The variance inflation factor doesn't indicate what is correlated with what so I looked at a correlations matrix. I consider a correlation of 0.4 or above to be high.
Total Charges is highly correlated with both Tenure and Monthly Charges and was not included in the model.
Before building the model:
- All features were standardized.
- The data was balanced.
The L1 norm was selected for Lasso.
Features were sorted by the absolute value of the coefficients in descending order.
Features with coefficients with the smallest absolute values were gradually removed which resulted in an increase in an increase in the area under the ROC curve of the test data. Once that value began to decrease no additional features were removed.
The best model had the largest AUC ROC for the test data.
Random Forest
Before building the model:
- All categorical features were label encoded.
- All features were standardized.
- The data was balanced.
My approach:
Using randomized search, I set a broad range of values for the following hyperparameters:
- maximum depth
- number of trees
- minimum samples an internal node must hold to further split
- minimum samples in a leaf
After that I narrowed my search and using grid search.
I selected the model with the largest AUC ROC for the test data.
The best model had 400 trees, a depth of 6, minimum sample split =20 and minimum sample leaf=13.
Gradient Boosting
Before building the model:
- All categorical features were label encoded.
- All features were standardized
My approach:
Using randomized search, I tuned for the following hyperparameters:
- maximum depth
- number of trees
- learning rate
I initiated my search for maximum depth and learning rate based on what I read in An Introduction to Statistical Learning. The authors indicate that a depth of one often works well and I initiated with [1,2]. For the learning rate, they say that the typical rates are 0.01 or 0.001 and I initiated with [0.01, 0.001]. Too many trees can lead to overfitting. I started with a range from 1,000 to 5,000.
I selected the model with the largest AUC ROC for the test data.
The best model had maximum depth = 1, learning rate = 0.01 and 5,000 trees. Models with more than 5,000 had lower values of AUC ROC.
Selecting the best model
The model with the highest AUC ROC and the highest accuracy in the test data is gradient boosting. However, in a churn model, the main objective is to detect all customers who will churn so that they can be incentivized with special offers to stay with the company. Even if the model predicts a customer that was going to leave the company, the customer will just get a special offer which is not a huge loss. Therefore, the most important criteria in selecting the best model is the Recall or the True Positive Rate of the test data.
Below are the confusion matrices of the test data for each of the three models. The row with the true values for Churn in the confustion matrix for Gradient Boosting looks quite different than it does for the other two models. That's because it has the lowest Recall.
The table below compares the three models.
In the data, there are only three numeric features. the others are categorical. When the features are primarily categorical, the relationship is most likely not linear.
Based on that reasoning, the best model is Random Forest.
- it's good at predicting nonlinear relationships
- the recall isn't that much lower than logistic regression
- the AUC ROC isn't that much lower than gradient boosting
Feature Importances
Random Forest top 15 feature importnaces
- Contract Type
- Customer Tenure
- Total Charges
- Monthly Charges
- Online Security
- Tech Support
- Internet Service
- Payment Method
- Online Backup
- Device Protection
- Paperless Billing
- Multiple Lines
- Gender
- Streaming Movies
- Dependents
About Author
