Credit card fraud is becoming a serious problem for the financial industry and can pose a considerable cost to banks, credit card issuers, and consumers. Fraud detection using data mining techniques has become an indispensable tool for banks and credit card companies to combat fraudulent transactions. A sample credit card data set contains the following variables: Fraud (1 if fraudulent activities, 0 otherwise), Amount (1 if low, 2 if medium, 3 if high), Online (1 if online transactions, 0 otherwise), and Prior (1 if products that the card holder previously purchased, 0 otherwise). A portion of the data set is shown in the accompanying table.

a. Create a bagging ensemble classification tree model to determine whether a transaction is fraudulent. What are the overall accuracy rate, sensitivity, and specificity of the model on the validation data? What is the AUC value of the model? 

b. Create a random forest ensemble classification tree model. Select two predictor variables randomly to construct each weak learner. What are the overall accuracy rate, sensitivity, and specificity of the model on the validation data? What is the AUC value of the model? Which is the most important predictor variable? 

c. Compare the two ensemble models. Which model shows more robust performance according to the lift value of the leftmost bar of the decile-wise lift chart?  

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Fraud 0 0 ⠀ 0 Amount 2 3 ⠀ 2 Online 0 0 ⠀ 0 Prior 1 0 ⠀ 1