Simulation.Rmd

---
title: "Simulation"
author: 'NULL'
date: "8/24/2021"
output: pdf_document
---

```{r}
# This is an example problem with p=20 covariates and sample size n=25. 
# The first 6 variables each have true coefficient of 1 and are normally
# distributed with a strong AR(1)-type correlation among them.  
# The remaining 14 variables are independent normals with no effect. 
```


```{r}
# Load the Libraries 
library(glmnet)
library(corrplot)
library(caret)
library(ggplot2)
library(pheatmap)
```

```{r}
# Load the Dataset
data = read.csv("C:\\Users\\sarmad\\Desktop\\data.csv", header = TRUE)
```

```{r}
str(data)
```

```{r}
summary(data)
```

```{r}
M = cor(data)
corrplot(M, method = 'number')
corrplot(M, method = 'color', order = 'alphabet') 
```

```{r}
d <- as.matrix(data)

# Default Heatmap
heatmap(d)
heatmap(d, Colv = NA, Rowv = NA, scale="column")
pheatmap(d, cutree_rows = 4)
```

```{r}
# Set seed
set.seed(123)

# Partition and create index matrix of selected values
index <- createDataPartition(data$target, p=0.7, list = FALSE, times = 1)

# Converting data to dataframe object
df <- as.data.frame(data)

# Create Train and Test dataframes
train_data <- df[index,]
test_data <- df[-index,]
```

```{r}
# k-fold cross validation (10 Folds) 

Control_specifications <- trainControl(method = "cv", number = 5,
                                       savePredictions = "all")
```

```{r}
# Specify and train LASSO Regression Model

# Create a vector of potential lambda values
lambda_vector <- 10^seq(5, -3, length=500)

# Set seed
set.seed(111)

# Specify LASSO Regression Model to be estimated using training data
model1 <- train(target ~ .,
                data = train_data,
                preProcess=c("center","scale"),
                method="glmnet",
                tuneGrid=expand.grid(alpha=1, lambda=lambda_vector),
                trControl=Control_specifications,
                na.action=na.omit)
```

```{r}
model1$bestTune$lambda
```

```{r}
round(coef(model1$finalModel, model1$bestTune$lambda), 3)
```

```{r}
# Plotting Log(lambda) & RMSE
plot(log(model1$results$lambda),
     model1$results$RMSE,
     col = "red",
     xlab = "log(lambda)",
     ylab = "RMSE")
```

```{r}
# Data Visualization of Variable Importance
ggplot(varImp(model1))
```
```{r}
# Model Prediction 
predictions1 <- predict(model1, newdata = test_data)
predictions1
```

```{r}
# Model Performance & Accuracy
Model_performance <- data.frame(RMSE=RMSE(predictions1, test_data$target),
                                Rsquared=R2(predictions1, test_data$target))
Model_performance
```

```{r}
# Set seed
set.seed(333)

# Specify Ridge Regression Model to be estimated using training data
model3 <- train(target ~ .,
                data = train_data,
                preProcess=c("center","scale"),
                method="glmnet",
                tuneGrid=expand.grid(alpha=0, lambda=lambda_vector),
                trControl=Control_specifications,
                na.action=na.omit)
```
```{r}
# Best optimal tuning parameter lambda
model3$bestTune$lambda
```

```{r}
# Rounding off for better visualization
round(coef(model3$finalModel, model3$bestTune$lambda), 3)
```

```{r}
# Plotting Log(lambda) & RMSE
plot(log(model3$results$lambda),
     model3$results$RMSE,
     col = "blue",
     xlab = "log(lambda)",
     ylab = "RMSE")
```
```{r}
# Data Visualization of Variable Importance
ggplot(varImp(model3))
```
```{r}
# Model Prediction 
predictions3 <- predict(model3, newdata = test_data)
predictions3
```

```{r}
# Model Performance & Accuracy
Model_performance3 <- data.frame(RMSE=RMSE(predictions3, test_data$target),
                                Rsquared=R2(predictions3, test_data$target))
Model_performance3
```

```{r}
# Set seed
set.seed(444)

# Specify Elastic-Net Regression Model to be estimated using training data
model4 <- train(target ~ .,
                data = train_data,
                preProcess=c("center","scale"),
                method="glmnet",
                tuneGrid=expand.grid(alpha=0.5, lambda=lambda_vector),
                trControl=Control_specifications,
                na.action=na.omit)
```

```{r}
# Best optimal tuning parameter lambda
model4$bestTune$lambda
```

```{r}
# Rounding off for better visualization
round(coef(model4$finalModel, model4$bestTune$lambda), 3)
```

```{r}
# Plotting Log(lambda) & RMSE
plot(log(model4$results$lambda),
     model4$results$RMSE,
     col = "green",
     xlab = "log(lambda)",
     ylab = "RMSE")
```
```{r}
# Data Visualization of Variable Importance
ggplot(varImp(model4))
```

```{r}
# Model Prediction 
predictions4 <- predict(model4, newdata = test_data)
predictions4
```

```{r}
# Model Performance & Accuracy
Model_performance4 <- data.frame(RMSE=RMSE(predictions4, test_data$target),
                                Rsquared=R2(predictions4, test_data$target))
Model_performance4
```

```{r}
library(grpreg)
group1 <- rep(1:20, each=1)
group1
```

```{r}
fit <- grpreg(train_data[1:20], train_data$target, group1, penalty = "grLasso")
plot(fit)
```


```{r}
coef(fit, lambda = 0.04230847)
```

```{r}
cvfit <- cv.grpreg(train_data[1:20], train_data$target, group1, penalty = "grLasso")
plot(cvfit)
```

```{r}
coef(cvfit)
```

```{r}
round(coef(cvfit), 3)
```


```{r}
summary(cvfit)
```

```{r}
cvfit$lambda.min
```

```{r}
predictions5 <- predict(fit, as.matrix(test_data[,1:20]), type = "response", lambda = cvfit$lambda.min)
predictions5
```

```{r}
Model_performance5 <- data.frame(RMSE=RMSE(predictions5, test_data$target),
                                Rsquared=R2(predictions5, test_data$target))
Model_performance5
```

```{r}
# Comparison of RMSE and R-square error for LASSO, OLS Multi Linear Regression model, RIDGE Regression, Elastic-Net Regression and Group Lasso. 
comp2 <- matrix(c(Model_performance$RMSE, Model_performance$Rsquared,
                 Model_performance3$RMSE, Model_performance3$Rsquared,
                 Model_performance4$RMSE, Model_performance4$Rsquared,
                 Model_performance5$RMSE, Model_performance5$Rsquared),
               ncol = 2, byrow = TRUE)
colnames(comp2) <- c("RMSE", "R-square")
rownames(comp2) <- c("LASSO Regression", "RIDGE Regression", "Elastic-Net Regression", "Group lasso")
comp2
```

```{r}
# Comparison of RMSE and R-square error for LASSO, OLS Multi Linear Regression model, RIDGE Regression, Elastic-Net Regression and Group Lasso.
comp2 <- as.table(comp2)
round(comp2, 4)

```