Tree-based models for joint Bernoulli/Log-normal distribution

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.

• The two-part tree procedure suggested by @TrynnaDoStat is very close to the tree-based version of a hurdle model. One part would be the binary zero hurdle (purchase yes/no) and the second part would be the model for the log(amount) of those who did purchase. The first part would be a binary classification tree (yielding predicted probabilities) and the second part would be a regression tree (yielding a predicted log-amount). In principle, any classification and regression tree procedure could be used that you feel comfortable with, e.g., in R rpart or partykit etc. Oct 16, 2015 at 19:57