Random Forest

LOADING DATA INTO R ENVIRONMENT

Reading the Data

# reading the data
df <- read.csv("DefaultData.csv")

Splitting data into training and test set

library(caret)
# data partition
set.seed(2341)
trainIndex <- createDataPartition(df$default, p = 0.80, list = FALSE)
# 80% training data
train.df <- df[trainIndex, ]
# 20% testing data
test.df <- df[-trainIndex, ]
dim(train.df)

## [1] 8001    4

dim(test.df)

## [1] 1999    4

TRAINING THE RANDOM FOREST MODEL

Setting Control parameters

library(caret)
# control parameters
trctrl <- trainControl(method = "none",classProbs = TRUE)

Running the Training Model

set.seed(123)
# fitting random forest classification model
RFModel <- train(default ~ ., 
                         data = train.df, 
                         method = "rf",
                         nbagg = 50,
                         trControl = trctrl)
# model summary
RFModel

## Random Forest 
## 
## 8001 samples
##    3 predictor
##    2 classes: 'No', 'Yes' 
## 
## No pre-processing
## Resampling: None

Variable Importance in Random Forest Model

# plotting variable importance
plot(varImp(RFModel))

TESTING THE RANDOM FOREST MODEL

Predicting Model on Test Data Set

# predicting the model on test data set
PredRFModel <- predict(RFModel, 
                    newdata = test.df,type = "prob")

Plotting the Predicted Probabilities

# plot of probabilities
plot(PredRFModel$Yes, 
     main = "Scatterplot of Probabilities of default (test data)", 
     xlab = "Customer ID", 
     ylab = "Predicted Probability of default")

Confusion Matrix at 50% Cut-Off Probability

# taking the cut-off probability 50%
pred.PredRFModel <- ifelse(PredRFModel$Yes > 0.50, "Yes", "No")

# saving predicted vector as factor 
Pred <- as.factor(pred.PredRFModel)

# ordering the vectors
Predicted <- ordered(Pred, levels = c("Yes", "No"))
Actual <- ordered(test.df$default,levels = c("Yes", "No"))

# making confusion matrix
cm <-confusionMatrix(data = Predicted,reference = Actual, positive = "Yes")
cm

## Confusion Matrix and Statistics
## 
##           Reference
## Prediction  Yes   No
##        Yes   19    5
##        No    47 1928
##                                          
##                Accuracy : 0.974          
##                  95% CI : (0.966, 0.9805)
##     No Information Rate : 0.967          
##     P-Value [Acc > NIR] : 0.04176        
##                                          
##                   Kappa : 0.4119         
##                                          
##  Mcnemar's Test P-Value : 1.303e-08      
##                                          
##             Sensitivity : 0.287879       
##             Specificity : 0.997413       
##          Pos Pred Value : 0.791667       
##          Neg Pred Value : 0.976203       
##              Prevalence : 0.033017       
##          Detection Rate : 0.009505       
##    Detection Prevalence : 0.012006       
##       Balanced Accuracy : 0.642646       
##                                          
##        'Positive' Class : Yes            
## 

Performance Metrics at different Cut-Off Probabilities

library(dplyr)

# function to print confusion matrices for diffrent cut-off levels of probability
CmFn <- function(cutoff) {
      
       # predicting the test set results
         PredRFModel <- predict(RFModel, test.df,type = "prob")
         C1 <- ifelse(PredRFModel$Yes > cutoff, "Yes", "No")
         C2 <- test.df$default
         predY   <- as.factor(C1)
           actualY <- as.factor(C2)
           Predicted <- ordered(predY, levels = c("Yes", "No"))
         Actual <- ordered(actualY,levels = c("Yes", "No")) 
     
        # use the confusionMatrix from the caret package
        cm1 <-confusionMatrix(data = Predicted,reference = Actual, positive = "Yes")
        # extracting accuracy
        Accuracy <- cm1$overall[1]
        # extracting sensitivity
          Sensitivity <- cm1$byClass[1]
        # extracting specificity
          Specificity <- cm1$byClass[2]
      # extracting value of kappa
          Kappa <- cm1$overall[2]
          
        # combined table
          tab <- cbind(Accuracy,Sensitivity,Specificity,Kappa)
        return(tab)}
     # sequence of cut-off points       
        cutoff1 <- seq( 0, 1, by = .05 )
     # loop using "lapply"
        tab2    <- lapply(cutoff1, CmFn)
     # creating matrix of different metrics
        numrows = length(cutoff1)
        pm <- matrix(1:numrows*4, nrow = numrows, ncol = 4)
     #  applying for loop
        for (i in 1:numrows){
          pm[i,] = tab2[[i]]}
        pm <- as.data.frame(pm)
        pm <- cbind(cutoff1, pm)
        pm <- rename(pm, cutoff =  cutoff1, Accuracy = V1, 
                       Senstivity = V2 ,Specificity = V3, kappa = V4)
    # printing the table
        print(pm)

##    cutoff  Accuracy Senstivity Specificity      kappa
## 1    0.00 0.8229115 0.86363636   0.8215210 0.19810577
## 2    0.05 0.9684842 0.59090909   0.9813761 0.53692652
## 3    0.10 0.9739870 0.53030303   0.9891361 0.56044755
## 4    0.15 0.9759880 0.53030303   0.9912054 0.58102857
## 5    0.20 0.9754877 0.50000000   0.9917227 0.56157768
## 6    0.25 0.9754877 0.50000000   0.9917227 0.56157768
## 7    0.30 0.9764882 0.46969697   0.9937920 0.55727446
## 8    0.35 0.9769885 0.43939394   0.9953440 0.54675670
## 9    0.40 0.9774887 0.42424242   0.9963787 0.54402141
## 10   0.45 0.9759880 0.36363636   0.9968960 0.48946495
## 11   0.50 0.9739870 0.28787879   0.9974133 0.41186588
## 12   0.55 0.9729865 0.22727273   0.9984480 0.34791591
## 13   0.60 0.9719860 0.16666667   0.9994827 0.27468284
## 14   0.65 0.9679840 0.04545455   0.9994827 0.08225133
## 15   0.70 0.9669835 0.00000000   1.0000000 0.00000000
## 16   0.75 0.9669835 0.00000000   1.0000000 0.00000000
## 17   0.80 0.9669835 0.00000000   1.0000000 0.00000000
## 18   0.85 0.9669835 0.00000000   1.0000000 0.00000000
## 19   0.90 0.9669835 0.00000000   1.0000000 0.00000000
## 20   0.95 0.9669835 0.00000000   1.0000000 0.00000000
## 21   1.00 0.9669835 0.00000000   1.0000000 0.00000000

ROC Curve using Package ROCR

# loading the package
library(ROCR)

## Warning: package 'ROCR' was built under R version 4.0.4

RFPrediction <- predict(RFModel, test.df,type = "prob")
Prediction <- prediction(RFPrediction[2],test.df$default)
performance <- performance(Prediction, "tpr","fpr")
# plotting ROC curve
plot(performance,main = "ROC Curve",col = 2,lwd = 2)
abline(a = 0,b = 1,lwd = 2,lty = 3,col = "black")

AUC (Area Under the Curve)

library(ROCR)
# area under curve
Prediction <- prediction(RFPrediction[2],test.df$default)
aucRF <- performance(Prediction, measure = "auc")
aucRF <- aucRF@y.values[[1]]
aucRF

## [1] 0.9013819