Credit Card Fraud: A Statistical Analysis on Detection Systems and its Effect on Prevention
Project Introduction
Credit card fraud occurs when there is an unauthorized use of a credit card to withdraw and transfer money or make purchases without the owner’s permission. This can occur by stealing someone’s physical credit card, phishing, or using stolen card data to make online purchases. Credit card fraud has been an ongoing problem for the past couple of decades with scammers developing newer tactics and all types of fraud becoming more common. When there are unresolved credit card fraud cases, the individuals’ credit scores could be affected which could cause long term damage such as unpaid debts or long-term debts opened in your name. Fortunately, in the past few years, technology has changed with more advanced security measures, two-factor authentication, and fraud alerts to prevent credit card fraud.Problem Statement
New forms of digital payments are always being introduced; however, it makes it easier for scammers to access sensitive information leading to an increase in credit card fraud. Theft of credit card information can be very stressful and a hassle to remedy to both the consumers and financial institutions. With the large number of card transactions that happen per day and new fraud tactics it is a struggle for current fraud detection systems to keep up. Better credit card fraud detection will ensure the protection of consumers’ sensitive financial information and reduce any loss for financial institutions.Project Objective
The main objective of this project is to analyze the effect of detection systems for fraudulent transactions. We will apply statistical methods to accurately detect fraud prevention. We aim to check credit card fraud systems’ effectiveness and see whether we need new and improved systems.Method: Logistic Regression
Describe the variables:
Dependent Variable: Fraud
Independent Variable: distance_from_home, distance_from_last_transaction, ratio_to_median_purchase_price, repeat_retailer, used_chip, used_pin_number, online_order.Install and Load the Libraries:
#if(!require(pROC)) install.packages("pROC")
#install.packages("Hmisc")
#install.packages("pscl")
#install.packages(pR2)
library(pscl)## Classes and Methods for R originally developed in the
## Political Science Computational Laboratory
## Department of Political Science
## Stanford University (2002-2015),
## by and under the direction of Simon Jackman.
## hurdle and zeroinfl functions by Achim Zeileis.library(Hmisc)##
## Attaching package: 'Hmisc'## The following objects are masked from 'package:base':
##
## format.pval, unitslibrary(pROC)## Type 'citation("pROC")' for a citation.##
## Attaching package: 'pROC'## The following objects are masked from 'package:stats':
##
## cov, smooth, varlibrary(readxl) Import Data:
data <- read_excel("~/Desktop/194A Group-Project/card_trans.data.xlsx")Descriptive Statistics and Visual Analysis
Data Summary:
summary(data)## distance_from_home distance_from_last_transaction
## Min. : 0.005 Min. : 0.000
## 1st Qu.: 3.878 1st Qu.: 0.297
## Median : 9.968 Median : 0.999
## Mean : 26.629 Mean : 5.037
## 3rd Qu.: 25.744 3rd Qu.: 3.356
## Max. :10632.724 Max. :11851.105
## ratio_to_median_purchase_price repeat_retailer used_chip
## Min. : 0.0044 Min. :0.0000 Min. :0.0000
## 1st Qu.: 0.4757 1st Qu.:1.0000 1st Qu.:0.0000
## Median : 0.9977 Median :1.0000 Median :0.0000
## Mean : 1.8242 Mean :0.8815 Mean :0.3504
## 3rd Qu.: 2.0964 3rd Qu.:1.0000 3rd Qu.:1.0000
## Max. :267.8029 Max. :1.0000 Max. :1.0000
## used_pin_number online_order fraud
## Min. :0.0000 Min. :0.0000 Min. :0.0000
## 1st Qu.:0.0000 1st Qu.:0.0000 1st Qu.:0.0000
## Median :0.0000 Median :1.0000 Median :0.0000
## Mean :0.1006 Mean :0.6506 Mean :0.0874
## 3rd Qu.:0.0000 3rd Qu.:1.0000 3rd Qu.:0.0000
## Max. :1.0000 Max. :1.0000 Max. :1.0000Interpretation: The average for distance_from_home is 10. The average for distance_from_last_transaction and ratio_to_median_purchase_price is 0.99. The average for used_chip, used_pin_number, and fraud are 0. And the average is 1 for repeat_retailed and online_order.Correlation Analysis:
corr <- rcorr(as.matrix(data))
corr## distance_from_home
## distance_from_home 1.00
## distance_from_last_transaction 0.00
## ratio_to_median_purchase_price 0.00
## repeat_retailer 0.14
## used_chip 0.00
## used_pin_number 0.00
## online_order 0.00
## fraud 0.19
## distance_from_last_transaction
## distance_from_home 0.00
## distance_from_last_transaction 1.00
## ratio_to_median_purchase_price 0.00
## repeat_retailer 0.00
## used_chip 0.00
## used_pin_number 0.00
## online_order 0.00
## fraud 0.09
## ratio_to_median_purchase_price repeat_retailer
## distance_from_home 0.00 0.14
## distance_from_last_transaction 0.00 0.00
## ratio_to_median_purchase_price 1.00 0.00
## repeat_retailer 0.00 1.00
## used_chip 0.00 0.00
## used_pin_number 0.00 0.00
## online_order 0.00 0.00
## fraud 0.46 0.00
## used_chip used_pin_number online_order fraud
## distance_from_home 0.00 0.0 0.00 0.19
## distance_from_last_transaction 0.00 0.0 0.00 0.09
## ratio_to_median_purchase_price 0.00 0.0 0.00 0.46
## repeat_retailer 0.00 0.0 0.00 0.00
## used_chip 1.00 0.0 0.00 -0.06
## used_pin_number 0.00 1.0 0.00 -0.10
## online_order 0.00 0.0 1.00 0.19
## fraud -0.06 -0.1 0.19 1.00
##
## n= 1000000
##
##
## P
## distance_from_home
## distance_from_home
## distance_from_last_transaction 0.8471
## ratio_to_median_purchase_price 0.1694
## repeat_retailer 0.0000
## used_chip 0.4858
## used_pin_number 0.1048
## online_order 0.1932
## fraud 0.0000
## distance_from_last_transaction
## distance_from_home 0.8471
## distance_from_last_transaction
## ratio_to_median_purchase_price 0.3113
## repeat_retailer 0.3533
## used_chip 0.0399
## used_pin_number 0.3688
## online_order 0.8880
## fraud 0.0000
## ratio_to_median_purchase_price repeat_retailer
## distance_from_home 0.1694 0.0000
## distance_from_last_transaction 0.3113 0.3533
## ratio_to_median_purchase_price 0.1695
## repeat_retailer 0.1695
## used_chip 0.5575 0.1787
## used_pin_number 0.3461 0.6764
## online_order 0.7415 0.5946
## fraud 0.0000 0.1746
## used_chip used_pin_number online_order fraud
## distance_from_home 0.4858 0.1048 0.1932 0.0000
## distance_from_last_transaction 0.0399 0.3688 0.8880 0.0000
## ratio_to_median_purchase_price 0.5575 0.3461 0.7415 0.0000
## repeat_retailer 0.1787 0.6764 0.5946 0.1746
## used_chip 0.1636 0.8268 0.0000
## used_pin_number 0.1636 0.7711 0.0000
## online_order 0.8268 0.7711 0.0000
## fraud 0.0000 0.0000 0.0000Interpretations:
1) Ratio to Median Purchase Price has the highest correlation with fraud suggesting that the possibility of fraud increases.
2) Online Order and Distance from Home have a positive correlation between online orders and distance from home variables with fraud. This means that they are more likely to be fraudulent.
3) Used Chip has a negative correlation between used-chip and fraud which indicates that transactions when chip is used have a lower possibility of fraud.
4) Linear Relationship as predictors have a straightforward relationship with the odds of fraud. Each transaction is independent of others. No Multicollinearity.
Binary Outcome Fraud has two possible values (fraud or no fraud).Scatter Plot Matrix:
pairs( ~ fraud + distance_from_home + distance_from_last_transaction
+ ratio_to_median_purchase_price + repeat_retailer + used_chip +
used_pin_number + online_order, data = data)
Interpretation: Using a scatter-plot matrix we are able to compare multiple variables at the same time with visualization.Data Analysis
Estimate Regression Model:
null_model <- glm(fraud ~ ratio_to_median_purchase_price + online_order
+ distance_from_home, data = data, family = binomial)## Warning: glm.fit: fitted probabilities numerically 0 or 1 occurrednull_model##
## Call: glm(formula = fraud ~ ratio_to_median_purchase_price + online_order +
## distance_from_home, family = binomial, data = data)
##
## Coefficients:
## (Intercept) ratio_to_median_purchase_price
## -9.10866 0.66722
## online_order distance_from_home
## 5.14165 0.01166
##
## Degrees of Freedom: 999999 Total (i.e. Null); 999996 Residual
## Null Deviance: 593000
## Residual Deviance: 332200 AIC: 332200Interpretation:
b0 = −9.11On average the risk of fraud decreases by 9.11 transactions by detection systems.
b1 = 0.67 The ratio to median purchase price does increases the risk of fraud by 0.67 transactions.
b2 = 5.14 Online orders does increases the risk of fraud by 5.14 transactions.
b3 = 0.01 Distance from home does increases the risk of fraud by 0.01.Odds Ratio:
coefficients <- summary(null_model)$coefficients
odds_ratio1 <- exp(coefficients["ratio_to_median_purchase_price", "Estimate"])
odds_ratio1## [1] 1.948811odds_ratio2 <- exp(coefficients["online_order", "Estimate"])
odds_ratio2## [1] 170.9969odds_ratio3 <- exp(coefficients["distance_from_home", "Estimate"])
odds_ratio3## [1] 1.011726Interpretation: odds ratios are greater than 1 indicate an increased possibility of fraudulent transactions. a 4% increase is associated with the ratio to the median purchase price, and a 12% increase is linked to online orders.Pseudo-R-squared:
pR2(null_model)## fitting null model for pseudo-r2## llh llhNull G2 McFadden r2ML
## -1.661204e+05 -2.964878e+05 2.607348e+05 4.397059e-01 2.295148e-01
## r2CU
## 5.130889e-01Interpretation: A McFadden value of 0.4397 shows that the model has a strong fit to the data, meaning it does a good job of explaining the variance and predicting the outcomes.Conclusion and Recommendation
Conclusion:
Based on our results, we came to the conclusion the detection systems that were put in place were not effective for combatting credit card fraud.
• As Our average was 9.11
Independent factors / variables still increased the risk of fraud.
• Our three variables: (β1, β2, β3) were not statistically significant as they are >0.05.Recommendations:
• Two factor-authentication when it comes to online orders
• Implementing Encryption Processes into different websites
• AI fraud detection (can monitor suspicious activity in real time & cross checking)
• Include security questions for higher purchases ($100+)