Variable importance in tree-based models

Tree-based models, either single trees or aggregates of trees, are usually judged and selected based on their prediction accuracy; new methods are developed with this same criterion. This has lead to a class of models that can be very useful tools for predicting a response variable, given a set of predictors, but is not often used for other modelling goals. Many of the assessments that we can make in a linear regression setting are much more difficult to make in tree-based models. While prediction goals may be well reached using these methods, the goals of understanding the roles of the variables and putting any sort of inferential statements, including confidence intervals, on useful summary measures from these tree-based models is still a wide open question. We develop tools that parallel those available in regression for descriptives, visualization of the model, summarizing the modelled effect of a variable, and evaluating the evidence supporting this assessment of the effect.