What are my options for estimating probabilities of success/failure?

Question

So, I want to estimate the probability that a student will succeed or fail in a particular major (suppose success means in this case to graduate with that major) based on data from that student's application. I have a lot of records of past students' application data and success.

I am aware that I could try logistic regression, but I would like to know all my options, including methods which allow more easily for non-linearities.

If I were just trying to classify incoming students, I think I would try an SVM model. But I don't know how easy it is to adapt that method to the task of estimating probabilities.

EDIT:

Much of the data is categorical. Often binary. Some features are real numbers / integers, as well.

Answer 1

You could consider classification trees. You don't say what software you are using, but there are several ways to do this in R, which is free. I personally have used the party() package with good results, but that's not to say other packages aren't just as good.

A classification tree is often very good at finding various interactions. You wind up with different sets of the IVs and the probability of "success" on your DV for different combinations.