Random forests with semiparametric cumulative probability models for continuous outcomes

Music City Center 

Regression models for continuous outcomes frequently require a transformation, which is often specified a priori or estimated from a parametric family. Cumulative probability models (CPMs) nonparametrically estimate the transformation by treating the continuous outcome as if it is ordinal. These models are especially useful for analyzing skewed outcomes and mixed outcomes (e.g., data with detection limits). The models give fitted distributions, upon which the fitted mean, median and quantiles can be computed. We now extend the CPMs by making the regressor side of the model nonparametric. Specifically, we have implemented random forest CPMs, in which each tree model has the regressor space partitioned into terminal nodes and then a CPM is fit on the partition. The fitted cumulative distribution functions are averaged across trees to obtain the final fitted distribution. We will evaluate the performance of this approach and demonstrate it in data applications.