Tree model with poisson distributed response variable If I understand correctly the R tree model - library(tree) - can only be used if the response variable is normally distributed. Is there a way to create a tree model with poisson distributed response variables? 
 A: As pointed out in previous comments: The CART algorithm (as implemented in tree or the rpart package) does not assume any likelihood for the data so that you can directly apply the algorithm to count responses as well. Using a transformation such as the square-root or continuity-corrected logs (log(... + 0.5)) or something similar might yield better results, though. It stabilizes the variances and avoids negative predictions (that would not be meaningful for count responses).
However, there are also model-based recursive partitioning algorithms that combine the nonparametric idea of recursive partitioning with formal parametric models. Prominent examples from the statistical literature are GUIDE introduced by Loh (2002, Statistica Sinica, 12, 361-386) or MOB by Zeileis et al. (2008, Journal of Computational and Graphical Statistics, 17(2), 492-514). The latter is implemented in R in the general mob() function from the partykit package with a convenience interface glmtree() for GLM-based trees. The latter can also be used in combination with family = poisson.
A simple example is the following. (Note that the Poisson assumption does not really make sense but the data is used for simplicity anyway.)
## Poisson GLM tree with constant fit (~ 1) in each segment (~ speed)
library("partykit")
m <- glmtree(dist ~ 1 | speed, data = cars, family = poisson)

## visualize constant-fit tree
plot(as.constparty(m))

## scatterplot with fitted mean
plot(dist ~ speed, data = cars)
lines(fitted(m) ~ speed, data = cars, col = "slategray", lwd = 2)



