I'm following the Getting Started with SAS Enterprise Miner example: https://support.sas.com/documentation/onlinedoc/miner/. If I do not adjust the prior probabilities to 0.05/0.95 as suggested, but use 0.25/0.75 instead, the regression and tree models produce models with ROC curves that appear to be y=x. In other words, they are like flipping a coin. It seems that the models place every observation in the class with the larger posterior probability. It would seem to me that adjusting the prior probabilities to 0.05/0.95 would make things worse. The help states, "Increasing the prior probability of a class increases the posterior probability, moving the classification boundary so that more cases are classified into the class." However, when you do that, the decision tree has splits and both the ROC curves are concave(ish). Why do the models produced with 0.05/0.95 priors produce "better" results than the models produced with 0.25/0.75 priors?
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