Hi, I'd like someone to please give me an explanation of the differences between goodness of fit and calibration and AUC vs. HL test.

As I understand it, both tests are needed to make sure your model is appropriate.

But I would like to back up and ask what they fundamentally are asking in conceptual terms.

Is calibration how well your "link" function fits the data and is goodness of fit how well everything fits the data?

I'm finding that increasing the AUC decreases the HL, but not always. It seems to be very random and I'm not sure if I should go for a high AUC at the expense of a lower HL, or if I should optimize both, or if it's just personal opinion?