# How good is a model if it can't predict a single positive class? [duplicate]

I have a training set of over a 100,000 points that is used to train a Logistic Regression Classifier (logit, since response is binary). The model is testing/fitted on a test set of 20,000 items. The test set is totally independent.

The ROC AUC value for this model is 0.85 which suggests that this is a good model. But I was not convinced. I picked a threshold $0.5$ (i.e., its classified positive if the model response $> 0.5$, negative if model response $< 0.5$).

At this threshold, I get the confusion matrix:

Confusion Matrix and Statistics

Reference
Prediction     0     1
0 33307   679
1     0     0

Accuracy : 0.98
95% CI : (0.9785, 0.9815)
No Information Rate : 0.98
P-Value [Acc > NIR] : 0.5102

Kappa : 0
Mcnemar's Test P-Value : <2e-16

Sensitivity : 0.00000
Specificity : 1.00000


So my question is, how good is the model if it is unable to predict a 'positive' class at 0.5 threshold?

My guess would be that the threshold of the model for labelling 'positive' is not $0.5$ in this case. Is this intuitive and make sense? Clearly the ROC AUC value is very high, which means that it does have a good TPR rate at lower thresholds.

• Why threshold 0.5 should be used? Why do not use estimated probabilities and take a decision at point where you get needed lift or if you have a profit function, at point of profit maximization? – Analyst Aug 20 '15 at 4:15