Bayesian Additive Regression Trees: Zero-inflated explanatory variable, will it influence the model and variable selection? I am currently implementing BART to model the distribution of a marine species (using the embarcadero package). I am using environmental covariates, but also some prey data that are very-much zero-inflated (already log-transformed). One example here, for the distribution of a variable that is retained by the model (x = Prey abundance, y= Presence/Absence of my species):

I am worried that this distribution influences the variable selection step in the model a lot, especially given that I have few observation of the species, and few observation of preys too. I fear it might lead to select these variables based on very little data, and discard other covariates of interest.
Do you know if there are typical assumption for explanatory variables distribution in BART?
I am considering removing the prey data from the model altogether and focus on the environmental covariates - and eventually examine the predator/prey co-occurrence using a different approach...
Another idea I had was to convert the prey data to binary presence/absence (to the cost of information on biomass), but I am not sure this would solve the issue given the number of 0s...
Thank you very much,

I think a solution to this is provided by Murray (2021) "Log-Linear Bayesian Additive Regression Trees for Multinomial Logistic and Count Regression Models" where a zero-inflated negative binomial BART (ZINB-BART) is outlined. The main point is to use a "data augmented" likelihood where we have an indicator function to account for the zero inflation.
In any case, I would suggest you monitor the acceptance rate per iteration, too low or too high values might indicate some fishy. Additionally, we should run posterior predictive checks on a hold-out test set to check if our observed data are "close" to our posterior predictive mean. Finally, when it comes to count data modelling, rootograms are our friends so utilise them too.
