Area under a ROC Curve after a logistic regression

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1

I am trying to compute ROCAnalysis.jl package to compute the AUC value after a logistic regression. When I ran

auc(roc(dep, pred)),

where dep is the vector with original binary dependent variable and pred the predicted values from the logistic regression.

I get a value very different from the AUC value I get from Stata. I am wondering whether there is a good documentation on how to use these functions.

2

The function seems to expect certain kind of scores for targets and non-targets, not truths and predictions. You can find other implementations in different packages. (General caution for beginners such as myself: it’s crucial to pay attention to how mature the packages are, and the more rough and abandoned it looks, the more you need to understand the source code to trust it.)

3

I’ve just had a nice needless romp through the finer details of ML implementations in Lux.jl because of my misunderstanding of ROCAnalysis.jl… Turns out I should read about things before using them.

There are some important points about this implementation of the ROC curve:

  1. The ROC curve is computed over False Negatives and False Positives, instead of True Positives and False Positives. So, your curve will be upside-down and a lower AUC is better.
  2. It takes target and non-target arrays as input. So, if you had y_hat as a vector of logits (or probabilities) and y_true as the 1/0 labels, then you’d use:
target = y_hat[y_true .== 1]
nontarget = y_hat[y_true .== 0]
roc(target, nontarget)

If you reverse the arguments, you’ll get a ROC curve that looks normal, but mirrored. Probably not ideal.

Anyways, after I figured all that out, I gave up on more packages and just used this:

function rocauc(y_true, y_pred)
    sorted_indices = sortperm(y_pred, rev=true)
    sorted_true, sorted_pred = y_true[sorted_indices], y_pred[sorted_indices]
    total_positive  = Int(sum(y_true))
    total_negative = length(y_true) - total_positive

    tpr, fpr, thresholds = [], [], []
    tp, fp = 0, 0
    for i in 1:length(y_true)
        isone(sorted_true[i]) ? (tp += 1) : (fp += 1)
        push!(tpr, tp / total_positive)
        push!(fpr, fp / total_negative)
        push!(thresholds, sorted_pred[i])
    end

    auc = sum((fpr[i] - fpr[i-1]) * (tpr[i] + tpr[i-1]) / 2 for i in 2:length(fpr))
    
    auc, fpr, tpr
end

Which will give you the normal AUC with y_true as described above and y_pred as the associated probabilities. If anyone wants to use it, you can print AUC and plot the ROC curve with:

using Plots
auc, fpr, tpr = rocauc(y_true, y_pred)
println("AUC: ", auc)
plot(fpr, tpr, 
     label="ROC w/ AUC = $(round(auc, digits=4))", 
     xlabel="False Positive Rate", 
     ylabel="True Positive Rate",
     title="ROC Curve"
)
4

If you want to compute the AUC after a logistic regression, try LogisticROC. lroc() function will give you both the plot and AUC value. lroc() takes the return value from a GLM model.