I have a large dataset which includes 36 variables (in %iles) to describe a student, and then the output is the students grades as a %ile. I am trying to predict, using the 36 variables, whether a student will fail out, ie. be in the bottom 2%ile.
My first attempt was a neural network with binary classification, forcing the model to predict that the student is either in the bottom 2%ile, or not. Having read a few posts on FHarrell.com, I was thinking that a binary logistic regression that outputs the probability of being in the bottom percentiles is better?
Or alternatively, should I just do a non-binary linear regression to directly predict the students %ile? The reason I thought that this wouldn't be as useful for my purposes is because I don't care about making predictions between any of the other percentiles. For example, I don't care about distinguishing between an A and a B student, I am just looking to identify F students. Therefore I would be losing accuracy in the bottom 2%ile and gaining it in the other irrelevant %iles?
Finally, I think that the neural network makes sense given that there is interaction between the variables. But if there is another model that I should consider please let me know.