instrumental_forest {grf}

Intrumental forest

Description

Trains an instrumental forest that can be used to estimate conditional local average treatment effects tau(X) identified using instruments. Formally, the forest estimates tau(X) = Cov[Y, Z | X = x] / Cov[W, Z | X = x]. Note that when the instrument Z and treatment assignment W coincide, an instrumental forest is equivalent to a causal forest.

Usage

instrumental_forest(
  X,
  Y,
  W,
  Z,
  Y.hat = NULL,
  W.hat = NULL,
  Z.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,
  reduced.form.weight = 0,
  tune.parameters = "none",
  tune.num.trees = 200,
  tune.num.reps = 50,
  tune.num.draws = 1000,
  compute.oob.predictions = TRUE,
  num.threads = NULL,
  seed = runif(1, 0, .Machine$integer.max)
)

Arguments

X

The covariates used in the instrumental regression.

Y

The outcome.

W

The treatment assignment (may be binary or real).

Z

The instrument (may be binary or real).

Y.hat

Estimates of the expected responses E[Y | Xi], marginalizing over treatment. If Y.hat = NULL, these are estimated using a separate regression forest. Default is NULL.

W.hat

Estimates of the treatment propensities E[W | Xi]. If W.hat = NULL, these are estimated using a separate regression forest. Default is NULL.

Z.hat

Estimates of the instrument propensities E[Z | Xi]. If Z.hat = NULL, these are estimated using a separate regression forest. Default is NULL.

num.trees

Number of trees grown in the forest. Note: Getting accurate confidence intervals generally requires more trees than getting accurate predictions. Default is 2000.

sample.weights

Weights given to each observation in estimation. If NULL, each observation receives equal weight. Default is NULL.

clusters

Vector of integers or factors specifying which cluster each observation corresponds to. Default is NULL (ignored).

equalize.cluster.weights

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.

sample.fraction

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.

mtry

Number of variables tried for each split. Default is \sqrt p + 20 where p is the number of variables.

min.node.size

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.

honesty

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.

honesty.fraction

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).

honesty.prune.leaves

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.

alpha

A tuning parameter that controls the maximum imbalance of a split. Default is 0.05.

imbalance.penalty

A tuning parameter that controls how harshly imbalanced splits are penalized. Default is 0.

stabilize.splits

Whether or not the instrument should be taken into account when determining the imbalance of a split. Default is TRUE.

ci.group.size

The forst 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.

reduced.form.weight

Whether splits should be regularized towards a naive splitting criterion that ignores the instrument (and instead emulates a causal forest).

tune.parameters

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 the honesty.* parameters are not tuned. Default is "none" (no parameters are tuned).

tune.num.trees

The number of trees in each 'mini forest' used to fit the tuning model. Default is 200.

tune.num.reps

The number of forests used to fit the tuning model. Default is 50.

tune.num.draws

The number of random parameter values considered when using the model to select the optimal parameters. Default is 1000.

compute.oob.predictions

Whether OOB predictions on training set should be precomputed. Default is TRUE.

num.threads

Number of threads used in training. By default, the number of threads is set to the maximum hardware concurrency.

seed

The seed of the C++ random number generator.

Value

A trained instrumental forest object.

References

Athey, Susan, Julie Tibshirani, and Stefan Wager. "Generalized Random Forests". Annals of Statistics, 47(2), 2019.

Examples

# Train an instrumental forest.
n <- 2000
p <- 5
X <- matrix(rbinom(n * p, 1, 0.5), n, p)
Z <- rbinom(n, 1, 0.5)
Q <- rbinom(n, 1, 0.5)
W <- Q * Z
tau <-  X[, 1] / 2
Y <- rowSums(X[, 1:3]) + tau * W + Q + rnorm(n)
iv.forest <- instrumental_forest(X, Y, W, Z)

# Predict on out-of-bag training samples.
iv.pred <- predict(iv.forest)

# Estimate a (local) average treatment effect.
average_treatment_effect(iv.forest)