I obtained a poor discrimination(AUROC) and a good callibration(according to hosmer lemeshow) in a logistic regression model. How can I address this situation?
1$\begingroup$ I would not rely on the HL test, in general. $\endgroup$– Todd DMar 2, 2017 at 4:52
$\begingroup$ Hosmer-Lemeshow test is considered obsolete: stats.stackexchange.com/questions/145112/… $\endgroup$– kjetil b halvorsen ♦Apr 13, 2017 at 9:22
Clearly, your explanatory variables doesn't explain the response very well - at least in the model you are using. You could try adding interaction terms, and/or use b-splines of the explanatory variables if they are continuous and their relationship to the response may be nonlinear.
1$\begingroup$ What is the range of values of the probabilities predicted by your model and how many observations do you have? $\endgroup$– user83346Mar 2, 2017 at 4:54
HL statistic gives you goodness-of-fit measure of your model, and in your case it's a good model.
When constructing the ROC curve, you plot the points with different probability thresholds. While you may have a well-fitted model, that doesn't necessary mean you have good classification performance over some of the thresholds. A possibility is the skewness of your data.