curves = function(actuals, predictions) {
    thresholds = c(unique(sort(predictions, decreasing = T)), min(predictions) - .Machine$double.eps)
    k = length(thresholds)
    tp = array(0, k)
    fn = array(0, k)
    fp = array(0, k)
    tn = array(0, k)
    for (i in 1:k) {
        tp[i] = sum((actuals == 1) & (predictions >  thresholds[i]))
        fn[i] = sum((actuals == 1) & (predictions <= thresholds[i]))
        fp[i] = sum((actuals == 0) & (predictions >  thresholds[i]))
        tn[i] = sum((actuals == 0) & (predictions <= thresholds[i]))
    }
    return(data.frame(thresholds, tp, fn, fp, tn,
                      fp.rate = fp / (fp + tn),
                      tp.rate = tp / (tp + fn),
                      precision = tp / (tp + fp)))
}

auc = function(x, y) {
    area = 0.0
    for (i in 2:length(x)) {
        # adding the area of the lower rectangle
        # plus half the area of the upper rectangle
        area = area + (x[i] - x[i - 1]) * (min(y[i], y[i - 1]) + 0.5 * abs(y[i] - y[i - 1]))
    }
    return(area)
}

set.seed(2^17-1)
library(ISLR)
index = sample(1:nrow(Default))
trn = Default[index[1:8000],]
tst = Default[index[8001:10000],]
model = glm(default ~ student + balance, data = trn, family = binomial)
predictions = predict(model, newdata = tst, type = "response")

evaluation = curves(as.integer(tst$default == "Yes"), predictions)
valid.precision = 2:nrow(evaluation)
par(mfrow = c(1, 2))
plot(evaluation$fp.rate, evaluation$tp.rate, type = "l")
title(paste("auc =", round(auc(evaluation$fp.rate, evaluation$tp.rate), 3)))
abline(a = 0, b = 1, lty = "dotted", col = "red")
legend("bottomright", legend = c("glm", "random"), lty = c("solid", "dashed"), col = c("black", "red"))
plot(evaluation$tp.rate[valid.precision], evaluation$precision[valid.precision], type = "l")
title(paste("auc =", round(auc(evaluation$tp.rate[valid.precision], evaluation$precision[valid.precision]), 3)))
abline(a = mean(tst$default == "Yes"), b = 0, lty = "dotted", col = "red")
legend("topright", legend = c("glm", "random"), lty = c("solid", "dashed"), col = c("black", "red"))