Transformation of Response in Regression Trees


After I calculated some multiple regressions I'd like to perform some simple
regression trees to capture also some possible nonlinear trends and discontinuities
in my data.

My multiple regression model is something like:
log(Y) ~ X1 + log(X2) + log(X3)

The response and some of the predictor variables are transformed to met
requirements of the regression. This is no problem so far and works well.

However, now I tried to find out if my response variable needs to be normal to
meet the requirements for basic regression trees. So far I read (and tested)
that the regression trees are invariant to any transformation of the predictors,
but what about the response? There are definitly differnent outcomes if I
transform the response (to get normal distributed data) or not.

Can anyone give some theoretical background/justification for (non)transforming
the response?


PS: I am doing all my analysis in R with tree() resp. rpart()