I'm fitting a logistic regression model to predict probabilities from a set of variables. I'm comparing two such models, say
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?
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?