A random forest approach for bounded outcome variables

Random forests have become an established tool for classication and regres-
sion, in particular in high-dimensional settings and in the presence of non-additive
predictor-response relationships. For bounded outcome variables restricted to the
unit interval, however, classical modeling approaches based on mean squared error
loss may severely suer as they do not account for heteroscedasticity in the data.
To address this issue, we propose a random forest approach for relating a beta dis-
tributed outcome to a set of explanatory variables. Our approach explicitly makes
use of the likelihood function of the beta distribution for the selection of splits dur-
ing the tree-building procedure. In each iteration of the tree-building algorithm it
chooses one explanatory variable in combination with a split point that maximizes
the log-likelihood function of the beta distribution with the parameter estimates de-
rived from the nodes of the currently built tree. Results of several simulation studies
and an application using data from the U.S.A. National Lakes Assessment Survey
demonstrate the properties and usefulness of the method, in particular when com-
pared to random forest approaches based on mean squared error loss and parametric
regression models.