For K treatments this "naive" multivariate-grf proceeeds by fitting K separate causal forests where in forest k the treatment assignment vector is one-hot encoded for treament k (i.e. treatment vector w_k entry i is one where individual i receives treatment k, else zero). The steps are:
Estimate propensities \(e_k(x)\) for each action 1..K: This is done with k separate regression forests with propensities normalized to sum to 1 at the final step.
Estimate the expected response m(x) = E(Y | X) marginalizing over treatment. This is done with one regression forest.
Estimate the treatment effect \(\tau_k(x) = \frac{\mu_k(x) - m(x)}{1 - e_k(x)}\) with a causal forest (where \(\mu_k(x) = E[Y | X, W=W_k]\))
multi_causal_forest(
X,
Y,
W,
Y.hat = NULL,
W.hat = NULL,
num.trees = 2000,
sample.weights = NULL,
clusters = NULL,
equalize.cluster.weights = FALSE,
sample.fraction = 0.5,
mtry = min(ceiling(sqrt(ncol(X)) + 20), ncol(X)),
min.node.size = 5,
honesty = TRUE,
honesty.fraction = 0.5,
honesty.prune.leaves = TRUE,
alpha = 0.05,
imbalance.penalty = 0,
stabilize.splits = TRUE,
ci.group.size = 2,
tune.parameters = "none",
tune.num.trees = 200,
tune.num.reps = 50,
tune.num.draws = 1000,
compute.oob.predictions = TRUE,
orthog.boosting = FALSE,
num.threads = NULL,
seed = runif(1, 0, .Machine$integer.max)
)The covariates used in the causal regression.
The outcome (must be a numeric vector with no NAs).
The treatment assignment (must be a categorical vector with no NAs).
Estimates of the expected responses E[Y | Xi], marginalizing over treatment. If Y.hat = NULL, these are estimated using a separate regression forest. See section 6.1.1 of the GRF paper for further discussion of this quantity. Default is NULL.
Matrix with estimates of the treatment propensities E[Wk | Xi]. If W.hat = NULL, these are estimated using a k separate regression forests. Default is NULL.
Number of trees grown in the forest. Note: Getting accurate confidence intervals generally requires more trees than getting accurate predictions. Default is 2000.
(experimental) Weights given to each sample in estimation. If NULL, each observation receives the same weight. Note: To avoid introducing confounding, weights should be independent of the potential outcomes given X. Default is NULL.
Vector of integers or factors specifying which cluster each observation corresponds to. Default is NULL (ignored).
If FALSE, each unit is given the same weight (so that bigger clusters get more weight). If TRUE, each cluster is given equal weight in the forest. In this case, during training, each tree uses the same number of observations from each drawn cluster: If the smallest cluster has K units, then when we sample a cluster during training, we only give a random K elements of the cluster to the tree-growing procedure. When estimating average treatment effects, each observation is given weight 1/cluster size, so that the total weight of each cluster is the same. Note that, if this argument is FALSE, sample weights may also be directly adjusted via the sample.weights argument. If this argument is TRUE, sample.weights must be set to NULL. Default is FALSE.
Fraction of the data used to build each tree. Note: If honesty = TRUE, these subsamples will further be cut by a factor of honesty.fraction. Default is 0.5.
Number of variables tried for each split. Default is \(\sqrt p + 20\) where p is the number of variables.
A target for the minimum number of observations in each tree leaf. Note that nodes with size smaller than min.node.size can occur, as in the original randomForest package. Default is 5.
Whether to use honest splitting (i.e., sub-sample splitting). Default is TRUE. For a detailed description of honesty, honesty.fraction, honesty.prune.leaves, and recommendations for parameter tuning, see the grf algorithm reference.
The fraction of data that will be used for determining splits if honesty = TRUE. Corresponds to set J1 in the notation of the paper. Default is 0.5 (i.e. half of the data is used for determining splits).
If true, prunes the estimation sample tree such that no leaves are empty. If false, keep the same tree as determined in the splits sample (if an empty leave is encountered, that tree is skipped and does not contribute to the estimate). Setting this to false may improve performance on small/marginally powered data, but requires more trees (note: tuning does not adjust the number of trees). Only applies if honesty is enabled. Default is TRUE.
A tuning parameter that controls the maximum imbalance of a split. Default is 0.05.
A tuning parameter that controls how harshly imbalanced splits are penalized. Default is 0.
Whether or not the treatment should be taken into account when determining the imbalance of a split. Default is TRUE.
The forest will grow ci.group.size trees on each subsample. In order to provide confidence intervals, ci.group.size must be at least 2. Default is 2.
A vector of parameter names to tune. If "all": all tunable parameters are tuned by cross-validation. The following parameters are tunable: ("sample.fraction", "mtry", "min.node.size", "honesty.fraction", "honesty.prune.leaves", "alpha", "imbalance.penalty"). If honesty is false these parameters are not tuned. Default is "none" (no parameters are tuned).
The number of trees in each 'mini forest' used to fit the tuning model. Default is 200.
The number of forests used to fit the tuning model. Default is 50.
The number of random parameter values considered when using the model to select the optimal parameters. Default is 1000.
Whether OOB predictions on training set should be precomputed. Default is TRUE.
(experimental) If TRUE, then when Y.hat = NULL or W.hat is NULL, the missing quantities are estimated using boosted regression forests. The number of boosting steps is selected automatically. Default is FALSE.
Number of threads used in training. By default, the number of threads is set to the maximum hardware concurrency.
The seed of the C++ random number generator.
A trained multi causal forest object (collection of causal forests). If tune.parameters is enabled,
then tuning information will be included through the tuning.output attribute of each forest.
# NOT RUN {
# Train a multi causal forest.
n <- 250
p <- 10
d <- 3
X <- matrix(rnorm(n * p), n, p)
W <- sample(c("A", "B", "C"), n, replace = TRUE)
Y <- X[, 1] + X[, 2] * (W == "B") + X[, 3] * (W == "C") + runif(n)
multi.forest <- multi_causal_forest(X = X, Y = Y, W = W)
# Predict using the forest.
multi.forest.pred <- predict(multi.forest)
head(multi.forest.pred$predictions)
# }
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