The HPFOREST Procedure

The incremental response modeling (IRM) method of analysis predicts how much a target value would change if a treatment were applied to the observation. For example, a conventional model might predict the probability of someone purchasing an item. An incremental response model would predict how much the probability of purchase would increase if the person were to receive a promotional coupon.

PROC HPFOREST provides an experimental implementation that uses a splitting criterion described in Su et al. (2009) and Radcliffe and Surry (2011). The treatment variable must be binary, and the target must have a binary or interval level of measurement.

A treatment variable differs from an input variable because the treatment is assigned at the discretion of some outside agent. The treatments must be assigned in such a way that input values associated with the response are balanced between the two treatment groups. If the data are not balanced, the predictions from many incremental response algorithms, including PROC HPFOREST, can be invalid. For example, if high values of an input X tend to produce high values in a target and a treatment value T is disproportionally assigned to observations that have high values of X, then PROC HPFOREST would incorrectly credit T with high values of the target.

Let T and C denote the two values of the treatment, and let L and R denote two branches of a tree node into which an observation can be assigned. PROC HPFOREST finds a split with the largest value of , where

For a binary target,

For an interval target,