How to Calculate AUC (Area Under Curve) in R?

In this article, we will discuss how to calculate the AUC (Area under Curve) of the ROC (Receiver Operating Characteristic) curve in the R Programming Language.

What is the AUC-ROC curve?

The ROC (Receiver Operating Characteristic) curve helps us to visualize the true positive rate or true negative rate of a prediction based on some model. This helps us to assess how well a regression model has fitted the data. The AUC (Area under Curve) of this ROC curve helps us to determine the specificity and sensitivity of the model. The closer the AUC value is to the 1, the better the given model fits the data.

pROC Package in r to Calculate AUC-ROC

To create the ROC (Receiver Operating Characteristic) curve object in the R Language, we use the roc() function of the pROC package library. The pROC is an R Language package to display and analyze ROC curves. The roc() function takes the actual and predicted value as an argument and returns a ROC curve object as a result. Then, to find the AUC (Area under Curve) of that curve, we use the auc() function. The auc() function takes the roc object as an argument and returns the area under the curve of that roc curve.

Syntax:

roc_object <- roc( response, prediction )

Parameters:

• response: determines the vector that contains the actual data.
• prediction: determines the vector that contains the data predicted by our model.

Installing and Loading the Libraries

Let's first install the package using the install.packages() function and then we will load the same using the library() function in R Programming Language.

install.packages("pROC")
library(pROC)

The area under the ROC curve of a logistic regression model.

Initializing the Dataset

Now let's create a sample dataset and then we will use it to train a model and then calculate the AUC-ROC of the model using pROC.

# sample data frame
df_train <- data.frame( x= c(1,2,3,4,5),
                  y= c(1,5,8,15,26),
                  z=c(0,1,1,0,0))
df_test <- data.frame( x= c(6,7,8),
                  y= c(38,45,72),
                  z=c(0,1,0))

Training Model and Calculating ROC

Now let's train a glm()  model on the dataset which we have created above and then make predictions using it. After we get the necessary predictions we will calculate the AUC-ROC value from it.

# fit logistic model
model <- glm(z ~ x+y, data=df_train)

# predicted data
prediction <- predict(model, df_test, 
                      type="response")

# create roc curve
roc_object <- roc( df_test$z, prediction)

# calculate area under curve
auc(roc_object)

Output:

Area under the curve: 0.5

Metrics Package in R to Calculate AUC-ROC

The Metrics package contains implementation for approximately all the evaluation metrics which are used in the supervised machine-learning tasks whether it is related to the regression, time-series, or classification-related task. In the below code implementation, we can observe how easy it is to calculate auc() using the Metrics Package in R.

Installing and Loading the Libraries

Let's first install the package using the install.packages() function and then we will load the same using the library() function in R.

install.packages("Metrics")
library(Metrics)

Initializing the Vectors

Now let's create two imaginary vectors with the actual target values and the predicted probabilities for the respective classes.

# Actual Target variable
actual <- c(0, 0, 1, 1, 1, 0, 0)

# Predicted probabilities for 
# the respective classes
predicted <- c(.1, .3, .4, .9,
               0.76, 0.55, 0.2)

Calculating AUC-ROC

Syntax:

auc(actual, predicted)

where,

• actual - The ground truth binary numeric vector containing 1 for the positive class and 0 for the negative class.
• predicted - A vector containing probabilities predicted by the model of each example being 1.

auc(actual, predicted)

Output:

0.916666666666667

MLtools Package in R to Calculate AUC-ROC

The mltools package contains helper functions that help majorly in exploratory data analysis. The main objective behind this function is that it provides highly optimized functions for speed and memory. In the below code implementation, we can observe how easy it is to calculate auc() using the Metrics Package in R.

Installing and Loading the Libraries

Let's first install the package using the install.packages() function and then we will load the same using the library() function in R.

install.packages("mltools")
library(mltools)

Initializing the Vectors

Now let's create two imaginary vectors with the actual target values and the predicted probabilities for the respective classes.

# Actual Target variable
actual <- c(0, 0, 1, 1, 1, 0, 0)

# Predicted probabilities for 
# the respective classes
predicted <- c(.1, .3, .4, .9,
               0.76, 0.55, 0.2)

Calculating AUC-ROC

Syntax:

auc_roc(actual, predicted, returnDT)

where,

• actual - The ground truth binary numeric vector containing 1 for the positive class and 0 for the negative class.
• predicted - A vector containing probabilities predicted by the model of each example being 1.
• returnDT - Returns a data.table object with False Positive Rate and True Positive Rate for plotting the ROC curve

auc_roc(predicted, actual)

Output:

0.916666666666667

auc_roc(predicted, actual, returnDT=TRUE)

Output: