Accumulated Local Effects (ALE) data from an rfsrc model

A partial dependence curve (gg_partial_rfsrc) marginalizes the forest's prediction by averaging over the joint distribution of the other predictors, a computation that is misleading when predictors are correlated, because it evaluates the forest at combinations of predictor values that never occur together in the data. Accumulated Local Effects (Apley and Zhu, 2020) avoid this by only ever perturbing a predictor within small local neighborhoods of its own observed values, then accumulating those local effects into a global curve.

Usage

gg_ale_rfsrc(
  rf_model,
  xvar.names,
  xvar2.name = NULL,
  newx = NULL,
  cat_limit = 10,
  n_eval = 25,
  which.class = 1
)

Arguments

rf_model: A fitted rfsrc object. Regression and classification forests only; survival is not yet implemented (see gg_shap, which has the same limitation).
xvar.names: Character vector of predictor names to compute ALE for. When xvar2.name is supplied, this must name exactly one predictor.
xvar2.name: Optional single character name of a second predictor. When supplied, second-order (interaction) ALE is computed for the pair xvar.names x xvar2.name instead of first-order ALE. Both predictors must be continuous in this version (see cat_limit).
newx: Optional data.frame of predictor values to evaluate ALE at. Defaults to the training data stored in rf_model$xvar. All column names must match rf_model$xvar.names.
cat_limit: Variables with fewer than cat_limit unique values in newx are treated as categorical; all others are continuous. Defaults to 10.
n_eval: Number of quantile bins used for a continuous predictor's ALE grid (first-order) or per axis (second-order). Defaults to 25.
which.class: For classification forests, the class (integer column index into the predicted-probability matrix) whose ALE is computed. Defaults to 1.

Value

For first-order ALE (xvar2.name = NULL), a named list with two elements, classed "gg_ale_rfsrc":

continuous: A data.frame with columns x (the bin edges, numeric), yhat (the centered ALE value at each edge), and name (variable name), for all continuous predictors.
categorical: The same columns but x kept as a factor in the model's level order, for low-cardinality predictors.

For second-order ALE (xvar2.name supplied), a data.frame classed "gg_ale_interaction" with columns x (grid values of xvar.names), y (grid values of xvar2.name), ale (the interaction surface value), name1, and name2.

Details

For a continuous predictor, gg_ale_rfsrc bins the observed values into n_eval quantile-based intervals. Within each bin, every observation's predictor value is replaced first with the bin's lower edge and then with its upper edge (all other predictors held at that observation's own values), and the average change in prediction is the bin's local effect. These local effects are accumulated (cumulatively summed) across bins and centered to have a weighted mean of zero, giving a curve that is directly comparable to gg_partial_rfsrc's output but immune to extrapolation into implausible predictor combinations.

For a categorical predictor, the model's own factor level order is used as the "grid": the local effect for the step from level $k$ to level $k+1$ is estimated only from observations actually at level $k+1$, comparing their prediction at that level against the counterfactual of level $k$. Relevel the predictor before fitting the forest to control this ordering.

Supplying xvar2.name switches to second-order (interaction) ALE between xvar.names and xvar2.name, isolating the part of their joint effect that is not explained by either variable's own main effect. It is the ALE analogue of an interaction term, computed on a 2-D grid of bins using the same local-perturbation idea, with the main effects removed via a row/column/grand weighted-mean decomposition (the same device used to isolate an interaction term in a two-way ANOVA). A purely additive forest returns an all-zero surface.

References

Apley, D. W. and Zhu, J. (2020). Visualizing the effects of predictor variables in black box supervised learning models. Journal of the Royal Statistical Society Series B, 82(4), 1059-1086.

Examples

## ------------------------------------------------------------
## regression, first-order ALE
## ------------------------------------------------------------
airq.obj <- randomForestSRC::rfsrc(Ozone ~ ., data = na.omit(airquality),
                                    ntree = 100)
ale_dta <- gg_ale_rfsrc(airq.obj, xvar.names = c("Wind", "Temp"))
plot(ale_dta)


# \donttest{
## ------------------------------------------------------------
## second-order (interaction) ALE between two continuous predictors
## ------------------------------------------------------------
ale_int <- gg_ale_rfsrc(airq.obj, xvar.names = "Wind",
                         xvar2.name = "Temp", n_eval = 15)
plot(ale_int)

# }