AnalysisDiscussion.Rmd

---
title: "R Notebook"
output:
  html_document: 
    toc: yes
  html_notebook: default
---
## Data Reading:
```{r}
library(readr)
Datav2 <- read_delim("Data/finalData.csv", ";", escape_double = FALSE, trim_ws = TRUE)
m2 <- read_delim("Data/cleanData.csv",";", escape_double = FALSE, trim_ws = TRUE)

library(readxl)
#Datav2 <- read_excel("E:/KPMG/KPMG/Data/prepdata.xlsx")
#m2 <- read_excel("E:/KPMG/KPMG/Data/prepdataOrg.xlsx")

```

# Data Stats
```{r}
Datav2$InterestType <- as.factor(Datav2$InterestType)
Datav2$MortgageType <- as.factor(Datav2$MortgageType)
Datav2$NewLoan <- as.factor(Datav2$NewLoan)
Datav2$ProbationaryLoans <- as.factor(Datav2$ProbationaryLoans)
Datav2$LTVCategory <- as.factor(Datav2$LTVCategory)
Datav2$InArrears <- as.factor(Datav2$InArrears)
#Datav2$County <- as.factor(Datav2$County)
Datav2$DefaultedLoans <- as.factor(Datav2$DefaultedLoans)
m2$InterestType <- as.factor(m2$InterestType)
m2$MortgageType <- as.factor(m2$MortgageType)
m2$NewLoan <- as.factor(m2$NewLoan)
m2$ProbationaryLoans <- as.factor(m2$ProbationaryLoans)
m2$LTVCategory <- as.factor(m2$LTVCategory)
m2$InArrears <- as.factor(m2$InArrears)
#m2$County <- as.factor(m2$County)
m2$DefaultedLoans <- as.factor(m2$DefaultedLoans)
m1 <- Datav2
m3 <- Datav2

```

# LR Model with Scaled data (Original Data Set)
## Data prep
##Data Subsetting
```{r}
set.seed(100)
dataPartition = sample(2,nrow(m2),replace=TRUE,prob=c(0.6,0.4))
m2train <- m2[dataPartition ==1,]
m2test <- m2[dataPartition ==2,]

```


##Simple GLM for all variables
```{r}
#m2glm <- glm(m2$DefaultedLoans ~., family = "binomial", data = m2train)
#step(m2glm)


#Simple glm with selected variables
m2glm <- glm(DefaultedLoans ~ CreditRating + InterestIncome + 
    PropertyValue + LoanBalance + AnnualPYMT + LTV + 
    InterestType + NewLoan + ProbationaryLoans + MortgageYears + 
    MortgageType + InArrears + County + AddressLatitude + AddressLongitude, 
    family = "binomial", data = m2train)
#step(m2glm)

summary(m2glm)

save(m2glm, file = "Model/m2glm.rda")

```

##Prediction
```{r}
m2test$prediction <- predict(m2glm, newdata=m2test, type="response")


#Confusion Matrix
table(m2test$DefaultedLoans, as.numeric(m2test$prediction >= 0.8))

confusion.glm <- function(data, model) {
  prediction <- ifelse(predict(model, data, type='response') > 0.5, TRUE, FALSE)
  confusion  <- table(prediction, as.logical(model$y))
  confusion  <- cbind(confusion, c(1 - confusion[1,1]/(confusion[1,1]+confusion[2,1]), 1 - confusion[2,2]/(confusion[2,2]+confusion[1,2])))
  confusion  <- as.data.frame(confusion)
  names(confusion) <- c('FALSE', 'TRUE', 'class.error')
  confusion
}

```

##Significant Variables
```{r}
significant.variables <- summary(m2glm)$coeff[-1,4] < 0.05
names(significant.variables)[significant.variables == TRUE]

```

##ROC
```{r}
#score test data set
library(ROCR)
m2test$lr_score <- predict(m2glm,type='response',m2test)
m2predlr <- prediction(m2test$lr_score, m2test$DefaultedLoans)
m2perflr <- performance(m2predlr,"tpr","fpr")



#ROC
plot(m2perflr, lwd=2, colorize=TRUE, main="ROC LR: Logistic Regression Performance")
lines(x=c(0, 1), y=c(0, 1), col="red", lwd=1, lty=3);
lines(x=c(1, 0), y=c(0, 1), col="green", lwd=1, lty=4)

```

##KS, Gini & AUC m2
```{r}
lr_KS <- round(max(attr(m2perflr,'y.values')[[1]]-attr(m2perflr,'x.values')[[1]])*100, 2)
lr_AUROC <- round(performance(m2predlr, measure = "auc")@y.values[[1]]*100, 2)
lr_Gini <- (2*lr_AUROC - 100)
cat("AUROC: ",lr_AUROC,"\tKS: ", lr_KS, "\tGini:", lr_Gini, "\n")

```


#LR without scaling
```{r}
#Data Subsetting
set.seed(100)
dataPartition = sample(2,nrow(m1),replace=TRUE,prob=c(0.6,0.4))
m1train <- m1[dataPartition ==1,]
m1test <- m1[dataPartition ==2,]
summary(m1)
```

##Simple GLM for all variables
```{r}
#m2glm <- glm(m1$DefaultedLoans ~., family = "binomial", data = m1train)
#step(m2glm)


#Simple glm with selected variables
m1glm <- glm(DefaultedLoans ~ CreditRating + InterestIncome + 
    PropertyValue + LoanBalance + AnnualPYMT + LTV + 
    InterestType + NewLoan + ProbationaryLoans + MortgageYears + 
    MortgageType + InArrears + County + AddressLatitude + AddressLongitude, 
    family = "binomial", data = m1train)
#step(m1glm)

summary(m1glm)

save(m1glm, file = "Model/m1glm.rda")
```

##Prediction
```{r}
m1test$prediction <- predict(m1glm, newdata=m1test, type="response")


#Confusion Matrix
table(m1test$DefaultedLoans, as.numeric(m1test$prediction >= 0.5))
```

##Significant Variables & ROC
```{r}
significant.variables <- summary(m1glm)$coeff[-1,4] < 0.05
names(significant.variables)[significant.variables == TRUE]

#ROC
#score test data set
library(ROCR)
m1test$lr_score <- predict(m1glm,type='response',m1test)
m1predlr <- prediction(m1test$lr_score, m1test$DefaultedLoans)
m1perflr <- performance(m1predlr,"tpr","fpr")


#ROC
plot(m1perflr, lwd=2, colorize=TRUE, main="ROC LR: Logistic Regression Performance")
lines(x=c(0, 1), y=c(0, 1), col="red", lwd=1, lty=3);
lines(x=c(1, 0), y=c(0, 1), col="green", lwd=1, lty=4)
```

##KS, Gini & AUC m1
```{r}
accuracy <- 89.01
lr_KS <- round(max(attr(m1perflr,'y.values')[[1]]-attr(m1perflr,'x.values')[[1]])*100, 2)
lr_AUROC <- round(performance(m1predlr, measure = "auc")@y.values[[1]]*100, 2)
lr_Gini <- (2*lr_AUROC - 100)
cat("Accuracy:",accuracy, "\tAUROC: ",lr_AUROC,"\tKS: ", lr_KS, "\tGini:", lr_Gini, "\n")
```





# Final Optimized Model
## Data prep
```{r}
m3 <- Datav2
m3$County <- as.factor(m3$County)
m3$LoanBalance <- scale(m3$LoanBalance)
m3$PropertyValue <- scale(m3$PropertyValue)
m3$AnnualPYMT <-scale(m3$AnnualPYMT)
m3$InterestIncome <-scale(m3$InterestIncome)
summary(m3)

```

##Data Subsetting
```{r}
set.seed(100)
dataPartition = sample(2,nrow(m3),replace=TRUE,prob=c(0.6,0.4))
m3train <- m3[dataPartition ==1,]
m3test <- m3[dataPartition ==2,]

```


##Simple GLM for all variables
```{r}
#m3glm <- glm(m3$DefaultedLoans ~., family = "binomial", data = m3train)
#step(m3glm)


#Simple glm with selected variables
m3glm <- glm(DefaultedLoans ~ CreditRating + InterestIncome + 
    PropertyValue + LoanBalance + AnnualPYMT + LTV + 
    InterestType + NewLoan + ProbationaryLoans + MortgageYears + 
    MortgageType + InArrears + County + AddressLatitude + AddressLongitude, 
    family = "binomial", data = m3train)
#step(m3glm)

summary(m3glm)

save(m3glm, file = "Model/m3glm.rda")

```

##Prediction
```{r}
m3test$prediction <- predict(m3glm, newdata=m3test, type="response")


#Confusion Matrix
table(m3test$DefaultedLoans, as.numeric(m3test$prediction >= 0.8))

confusion.glm <- function(data, model) {
  prediction <- ifelse(predict(model, data, type='response') > 0.5, TRUE, FALSE)
  confusion  <- table(prediction, as.logical(model$y))
  confusion  <- cbind(confusion, c(1 - confusion[1,1]/(confusion[1,1]+confusion[2,1]), 1 - confusion[2,2]/(confusion[2,2]+confusion[1,2])))
  confusion  <- as.data.frame(confusion)
  names(confusion) <- c('FALSE', 'TRUE', 'class.error')
  confusion
}

```

##Significant Variables
```{r}
significant.variables <- summary(m3glm)$coeff[-1,4] < 0.05
names(significant.variables)[significant.variables == TRUE]

```

##ROC
```{r}
#score test data set
library(ROCR)
m3test$lr_score <- predict(m3glm,type='response',m3test)
m3predlr <- prediction(m3test$lr_score, m3test$DefaultedLoans)
m3perflr <- performance(m3predlr,"tpr","fpr")



#ROC
plot(m3perflr, lwd=2, colorize=TRUE, main="ROC LR: Logistic Regression Performance")
lines(x=c(0, 1), y=c(0, 1), col="red", lwd=1, lty=3);
lines(x=c(1, 0), y=c(0, 1), col="green", lwd=1, lty=4)

```

##KS, Gini & AUC m3
```{r}
lr_KS <- round(max(attr(m3perflr,'y.values')[[1]]-attr(m3perflr,'x.values')[[1]])*100, 2)
lr_AUROC <- round(performance(m3predlr, measure = "auc")@y.values[[1]]*100, 2)
lr_Gini <- (2*lr_AUROC - 100)
cat("AUROC: ",lr_AUROC,"\tKS: ", lr_KS, "\tGini:", lr_Gini, "\n")

```

# ########################################################################################
# # 
# #   Desicion Tree
```{r}
library(rpart)
library(rattle)					# Fancy tree plot
library(rpart.plot)			# Enhanced tree plots
library(RColorBrewer)		# Color selection for fancy tree plot
library(party)					# Alternative decision tree algorithm
library(partykit)				# Convert rpart object to BinaryTree
library(caret)
library(tree)
```

#Decision tree with original dataset
```{r}
m2dt <- rpart(DefaultedLoans ~ CreditRating + InterestIncome + 
    PropertyValue + LoanBalance + AnnualPYMT + LTV + 
    InterestType + NewLoan + ProbationaryLoans + MortgageYears + 
    MortgageType + InArrears + County + AddressLatitude + AddressLongitude,
    method = "class",data=m2train, control =  rpart.control(minisplit=5,cp = 0.001))

m2test$DT_score <- predict(m2dt,type='prob',m2test)
DT_prediction2 <- prediction(m2test$DT_score[,2],m2test$DefaultedLoans)
DT_performance2 <- performance(DT_prediction2,"tpr","fpr")

# MOdel performance plot
plot(DT_performance2, lwd=2, colorize=TRUE, main="ROC Decision Tree: Traditional Recursive Partitioning")
lines(x=c(0, 1), y=c(0, 1), col="red", lwd=1, lty=3);
lines(x=c(1, 0), y=c(0, 1), col="green", lwd=1, lty=4)
```
# Confusion Matrix
```{r}
defaultPredict <- predict(m2dt,m2test, type = 'class')
matrix <- table(defaultPredict, m2test$DefaultedLoans)
print(matrix)
```

# KS & AUC DT
```{r}
DT_AUROC <- round(performance(DT_prediction2, measure = "auc")@y.values[[1]]*100, 2)
DT_KS <- round(max(attr(DT_performance2,'y.values')[[1]]-attr(DT_performance2,'x.values')[[1]])*100, 2)
DT_Gini <- (2*DT_AUROC - 100)
cat("AUROC: ",DT_AUROC,"\tKS: ", DT_KS, "\tGini:", DT_Gini, "\n")
```

# Decision tree without scaling variables
```{r}

m1dt <- rpart(DefaultedLoans ~ CreditRating + InterestIncome + 
    PropertyValue + LoanBalance + AnnualPYMT + LTV + 
    InterestType + NewLoan + ProbationaryLoans + MortgageYears + 
    MortgageType + InArrears + County + AddressLatitude + AddressLongitude,method = "class",data=m1train, control =  rpart.control(minisplit=5,cp = 0.001))


m1test$DT_score <- predict(m1dt,type='prob',m1test)
DT_prediction1 <- prediction(m1test$DT_score[,2],m1test$DefaultedLoans)
DT_performance1 <- performance(DT_prediction1,"tpr","fpr")

# MOdel performance plot
plot(DT_performance1, lwd=2, colorize=TRUE, main="ROC Decision Tree: Traditional Recursive Partitioning")
lines(x=c(0, 1), y=c(0, 1), col="red", lwd=1, lty=3);
lines(x=c(1, 0), y=c(0, 1), col="green", lwd=1, lty=4)
```
# Confusion Matrix
```{r}
defaultPredict <- predict(m1dt,m1test, type = 'class')
matrix <- table(defaultPredict, m1test$DefaultedLoans)
print(matrix)
write.csv(m1test, "Data/m1test.csv")
```

# KS & AUC DT
```{r}
DT_AUROC <- round(performance(DT_prediction1, measure = "auc")@y.values[[1]]*100, 2)
DT_KS <- round(max(attr(DT_performance1,'y.values')[[1]]-attr(DT_performance1,'x.values')[[1]])*100, 2)
DT_Gini <- (2*DT_AUROC - 100)
cat("AUROC: ",DT_AUROC,"\tKS: ", DT_KS, "\tGini:", DT_Gini, "\n")
```
# Final optimized decision tree
```{r}
m3dt <- rpart(DefaultedLoans ~ CreditRating + InterestIncome + 
    PropertyValue + LoanBalance + AnnualPYMT + LTV + 
    InterestType + NewLoan + ProbationaryLoans + MortgageYears + 
    MortgageType + InArrears + County + AddressLatitude + AddressLongitude,method = "class",data=m3train, control =  rpart.control(minisplit=5,cp = 0.001))

m3test$DT_score <- predict(m3dt,type='prob',m3test)
DT_prediction3 <- prediction(m3test$DT_score[,2],m3test$DefaultedLoans)
DT_performance3 <- performance(DT_prediction3,"tpr","fpr")

# MOdel performance plot
plot(DT_performance3, lwd=2, colorize=TRUE, main="ROC Decision Tree: Traditional Recursive Partitioning")
lines(x=c(0, 1), y=c(0, 1), col="red", lwd=1, lty=3);
lines(x=c(1, 0), y=c(0, 1), col="green", lwd=1, lty=4)
```
# Confusion Matrix
```{r}
defaultPredict <- predict(m3dt,m3test, type = 'class')
matrix <- table(defaultPredict, m3test$DefaultedLoans)
print(matrix)
write.csv(m3test, "Data/m3test.csv")
```

# KS & AUC DT
```{r}
DT_AUROC <- round(performance(DT_prediction3, measure = "auc")@y.values[[1]]*100, 2)
DT_KS <- round(max(attr(DT_performance3,'y.values')[[1]]-attr(DT_performance3,'x.values')[[1]])*100, 2)
DT_Gini <- (2*DT_AUROC - 100)
cat("AUROC: ",DT_AUROC,"\tKS: ", DT_KS, "\tGini:", DT_Gini, "\n")
```

#Results

## Performance of Original Dataset
```{r}
#Original
plot(m2perflr, col='blue', lty=1, main='ROCs: Model Performance Comparision(Original Data') # Modified data(without scaling)
plot(DT_performance2, col='red',lty=2, add=TRUE); # Original Data Set
    legend(0.6,0.5,
           c('Logistic Regression','Decision tree'),
           col=c('blue', "red"),
           lwd=3);
lines(c(0,1),c(0,1),col = "gray", lty = 4 ) # random line
```

## Modified Data (Unnormalized data)
```{r}
#Without Scaling
plot(m1perflr, col='blue', lty=1, main='ROCs: Model Performance Comparision (Unnormalized Data)') # Modified data(without scaling)
plot(DT_performance1, col='red',lty=2, add=TRUE); # Original Data Set
    legend(0.6,0.5,
           c('Logistic Regression','Decision tree'),
           col=c('blue',"red"),
           lwd=3);
lines(c(0,1),c(0,1),col = "gray", lty = 4 ) # random line
```

## Modified Data (Normalized data)
```{r}
#Final
plot(m3perflr, col='blue', lty=1, main='ROCs: Model Performance Comparision(Normalized Data') # Modified data(without scaling)
plot(DT_performance3, col='red',lty=2, add=TRUE); # Original Data Set
    legend(0.6,0.5,
           c('Logistic Regression','Decision tree'),
           col=c('blue', "red"),
           lwd=3);
lines(c(0,1),c(0,1),col = "gray", lty = 4 ) # random line
```
#Logistic Regression

##KS, Gini & AUC m2
```{r}
lr_KS <- round(max(attr(m2perflr,'y.values')[[1]]-attr(m2perflr,'x.values')[[1]])*100, 2)
lr_AUROC <- round(performance(m2predlr, measure = "auc")@y.values[[1]]*100, 2)
lr_Gini <- (2*lr_AUROC - 100)
cat("AUROC: ",lr_AUROC,"\tKS: ", lr_KS, "\tGini:", lr_Gini, "\n")

```

##KS, Gini & AUC m1
```{r}
accuracy <- 89.01
lr_KS <- round(max(attr(m1perflr,'y.values')[[1]]-attr(m1perflr,'x.values')[[1]])*100, 2)
lr_AUROC <- round(performance(m1predlr, measure = "auc")@y.values[[1]]*100, 2)
lr_Gini <- (2*lr_AUROC - 100)
cat("Accuracy:",accuracy, "\tAUROC: ",lr_AUROC,"\tKS: ", lr_KS, "\tGini:", lr_Gini, "\n")
```

##KS, Gini & AUC m3
```{r}
lr_KS <- round(max(attr(m3perflr,'y.values')[[1]]-attr(m3perflr,'x.values')[[1]])*100, 2)
lr_AUROC <- round(performance(m3predlr, measure = "auc")@y.values[[1]]*100, 2)
lr_Gini <- (2*lr_AUROC - 100)
cat("AUROC: ",lr_AUROC,"\tKS: ", lr_KS, "\tGini:", lr_Gini, "\n")

```


# KS & AUC DT Original
```{r}
DT_AUROC <- round(performance(DT_prediction2, measure = "auc")@y.values[[1]]*100, 2)
DT_KS <- round(max(attr(DT_performance2,'y.values')[[1]]-attr(DT_performance2,'x.values')[[1]])*100, 2)
DT_Gini <- (2*DT_AUROC - 100)
cat("AUROC: ",DT_AUROC,"\tKS: ", DT_KS, "\tGini:", DT_Gini, "\n")
```
# KS & AUC DT
```{r}
DT_AUROC <- round(performance(DT_prediction1, measure = "auc")@y.values[[1]]*100, 2)
DT_KS <- round(max(attr(DT_performance1,'y.values')[[1]]-attr(DT_performance1,'x.values')[[1]])*100, 2)
DT_Gini <- (2*DT_AUROC - 100)
cat("AUROC: ",DT_AUROC,"\tKS: ", DT_KS, "\tGini:", DT_Gini, "\n")
```

# KS & AUC DT
```{r}
DT_AUROC <- round(performance(DT_prediction3, measure = "auc")@y.values[[1]]*100, 2)
DT_KS <- round(max(attr(DT_performance3,'y.values')[[1]]-attr(DT_performance3,'x.values')[[1]])*100, 2)
DT_Gini <- (2*DT_AUROC - 100)
cat("AUROC: ",DT_AUROC,"\tKS: ", DT_KS, "\tGini:", DT_Gini, "\n")
```