Can AUC decrease with additional variables? I'm fitting a logistic regression model to predict probabilities from a set of variables. I'm comparing two such models, say M1 and M2. The only difference is that M2 includes all the variables of M1 plus a few more variables. The idea is to see which variables are useful in predicting my dependent variable. 
I expected that AUCs should be non-decreasing with the addition of new variables. If the new variables have predictive power, they should increase the AUC, if they don't, then the AUC should be unaffected. But I find that AUC actually decreases as I add a particular set of new variables. What could be the issue here?
I'm using predict() to get the predicted probabilities. Does it automatically drop all the statistically insignificant variables when calculating the predicted value? Could this be the cause of the drop in AUC? 
 A: The effect of uninformative features depends largely on your modeling strategy. For some approaches they are irrelevant while for others they can dramatically decrease overall performance.
Your intuition that using more features should necessarily yield a better model is wrong.
A: 4 years late but I just had the same experience now.
For logistic regression, the model should be smart enough to disregard useless variables. There is no constraint preventing the coefficients of these variables from being 0. 
It is important to remember how a logistic regression works. I believe the model optimises squared error not AUC directly. You might want to check if your MSE improved when your AUC deteriorated. In my case my MSE did improve despite my AUC getting worse.
I did notice that there is sometimes a very small increase in my MSE with more features. I think it might be one of the model default parameters maybe maximum iterations or a tolerance criteria for convergence. BTW i am using logistic regression from sklearn.
A: Check if you have not missings values in the new variables. Logistic regression reject the cases with missing data, and only adjust the model for full cases. You must sure that you are comparing the discrimination in the same cohorts.
