I'm working on trying to model the profitability of a set of customers given a vector of behaviors.
This data includes both customers who did and did not make a purchase. As a result, the DV (profit) is heavily zero-inflated. I've used hurdle models to capture the joint distribution of this outcomes, but in my current problem, I'm currently restricted to only using a tree based model. To that extent, I can only use a single tree.
Are there any tree based models that can accommodate this type of joint distribution?
One possible solution I thought of is to change all of the zeros to an extreme negative number (e.g., -9999). This will max the difference between any observation with a positive value and any zero to try and manipulate the distance. My hope is that I can artificially force a majority of the 0's into a single node and have the algorithm do it's best to discriminate profit values within the non-zero node.