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A Random Forest Approach for Modeling Bounded Outcomes
Random forests have become an established tool for classification and
regression, in particular in high-dimensional settings and in the presence of
complex predictor-response relationships. For bounded outcome variables
restricted to the unit interval, however, classical random forest approaches
may severely suffer as they do not account for the heteroscedasticity in the
data. A random forest approach is proposed for relating beta distributed
outcomes to explanatory variables. The approach explicitly makes use of the
likelihood function of the beta distribution for the selection of splits during
the tree-building procedure. In each iteration of the tree-building algorithm
one chooses the combination of explanatory variable and splitting rule that
maximizes the log-likelihood function of the beta distribution with the
parameter estimates derived from the nodes of the currently built tree. Several
simulation studies demonstrate the properties of the method and compare its
performance to classical random forest approaches as well as to parametric
regression models.Comment: 19 pages, 5 figure