Estimate the strength of interaction effects

Computes Friedman's H-statistic to assess the strength of variable interactions.

Usage

interact.gbm(x, data, i.var = 1, n.trees = x$n.trees)

Arguments

x: A gbm.object fitted using a call to gbm.
data: The dataset used to construct x. If the original dataset is large, a random subsample may be used to accelerate the computation in interact.gbm.
i.var: A vector of indices or the names of the variables for compute the interaction effect. If using indices, the variables are indexed in the same order that they appear in the initial gbm formula.
n.trees: The number of trees used to generate the plot. Only the first n.trees trees will be used.

Value

Returns the value of $H$.

Details

interact.gbm computes Friedman's H-statistic to assess the relative strength of interaction effects in non-linear models. H is on the scale of [0-1] with higher values indicating larger interaction effects. To connect to a more familiar measure, if $x_1$ and $x_2$ are uncorrelated covariates with mean 0 and variance 1 and the model is of the form $$y=\beta_0+\beta_1x_1+\beta_2x_2+\beta_3x_3$$ then $$H=\frac{\beta_3}{\sqrt{\beta_1^2+\beta_2^2+\beta_3^2}}$$

Note that if the main effects are weak, the estimated H will be unstable. For example, if (in the case of a two-way interaction) neither main effect is in the selected model (relative influence is zero), the result will be 0/0. Also, with weak main effects, rounding errors can result in values of H > 1 which are not possible.

References

J.H. Friedman and B.E. Popescu (2005). “Predictive Learning via Rule Ensembles.” Section 8.1

Author

Greg Ridgeway gregridgeway@gmail.com