Logistic Regression is a statistical method that we use to fit a regression model when the response variable is binary. To assess how well a logistic regression model fits a dataset, we can look at the following two metrics:

**Sensitivity:**The probability that the model predicts a positive outcome for an observation when indeed the outcome is positive.**Specificity:**The probability that the model predicts a negative outcome for an observation when indeed the outcome is negative.

One easy way to visualize these two metrics is by creating a **ROC curve**, which is a plot that displays the sensitivity and specificity of a logistic regression model.

This tutorial explains how to create and interpret a ROC curve in R using the ggplot2 visualization package.

**Example: ROC Curve Using ggplot2**

Suppose we fit the following logistic regression model in R:

#loadDefaultdataset from ISLR book data <- ISLR::Default #divide dataset into training and test set set.seed(1) sample <- sample(c(TRUE, FALSE), nrow(data), replace=TRUE, prob=c(0.7,0.3)) train <- data[sample, ] test <- data[!sample, ] #fit logistic regression model to training set model <- glm(default~student+balance+income, family="binomial", data=train) #use model to make predictions on test set predicted <- predict(model, test, type="response")

To visualize how well the logistic regression model performs on the test set, we can create a ROC plot using the **ggroc()** function from the pROC package:

#load necessary packages library(ggplot2) library(pROC) #define object to plot rocobj <- roc(test$default, predicted) #create ROC plot ggroc(rocobj)

The y-axis displays the sensitivity (the true positive rate) of the model and the x-axis displays the specificity (the true negative rate) of the model.

Note that we can add some styling to the plot and also provide a title that contains the AUC (area under the curve) for the plot:

#load necessary packages library(ggplot2) library(pROC) #define object to plot and calculate AUC rocobj <- roc(test$default, predicted) auc <- round(auc(test$default, predicted),4) #create ROC plot ggroc(rocobj, colour = 'steelblue', size = 2) + ggtitle(paste0('ROC Curve ', '(AUC = ', auc, ')'))

Note that we can also modify the theme of the plot:

#create ROC plot with minimal theme ggroc(rocobj, colour = 'steelblue', size = 2) + ggtitle(paste0('ROC Curve ', '(AUC = ', auc, ')')) + theme_minimal()

Refer to this article for a guide to the best ggplot2 themes.

Is there an article that explains what the ROC results mean? So did this model do well? If so, what are next steps? If not, what are next steps? Any assistance in helping me understand this will be appreciated!