# double_robust_scores: Matrix Gamma of scores for each treatment a In policytree: Policy Learning via Doubly Robust Empirical Welfare Maximization over Trees

## Description

Computes a matrix of double robust scores Γ_{ia} = μ_a(x) + \frac{1}{e_a(x)} (Y_i - μ_a(x)) 1(A_i=a)

## Usage

  1 2 3 4 5 6 7 8 9 10 ## S3 method for class 'causal_forest' double_robust_scores(object, ...) ## S3 method for class 'instrumental_forest' double_robust_scores(object, compliance.score = NULL, ...) ## S3 method for class 'multi_arm_causal_forest' double_robust_scores(object, outcome = 1, ...) double_robust_scores(object, ...) 

## Arguments

 object An appropriate causal forest type object ... Additional arguments compliance.score An estimate of the causal effect of Z on W. i.e., Delta(X) = E(W | X, Z = 1) - E(W | X, Z = 0), for each sample i = 1, ..., n. If NULL (default) then this is estimated with a causal forest. outcome Only used with multi arm causal forets. In the event the forest is trained with multiple outcomes Y, a column number/name specifying the outcome of interest. Default is 1.

## Details

This is the matrix used for CAIPWL (Cross-fitted Augmented Inverse Propensity Weighted Learning)

## Value

A matrix of scores for each treatment

## Methods (by class)

• causal_forest: Scores (Γ_0, Γ_1)

• instrumental_forest: Scores (-Γ, Γ)

• multi_arm_causal_forest: Matrix Γ of scores for each treatment a

## Note

For instrumental_forest this method returns (-Γ_i, Γ_i) where Γ_i is the double robust estimator of the treatment effect as in eqn. (44) in Athey and Wager (2021).

## References

Athey, Susan, and Stefan Wager. "Policy Learning With Observational Data." Econometrica 89.1 (2021): 133-161.

## Examples

  1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 # Compute double robust scores for a multi-arm causal forest n <- 500 p <- 10 X <- matrix(rnorm(n * p), n, p) W <- as.factor(sample(c("A", "B", "C"), n, replace = TRUE)) Y <- X[, 1] + X[, 2] * (W == "B") + X[, 3] * (W == "C") + runif(n) forest <- grf::multi_arm_causal_forest(X, Y, W) scores <- double_robust_scores(forest) head(scores) # Compute double robust scores for a causal forest n <- 500 p <- 10 X <- matrix(rnorm(n * p), n, p) W <- rbinom(n, 1, 0.5) Y <- pmax(X[, 1], 0) * W + X[, 2] + pmin(X[, 3], 0) + rnorm(n) c.forest <- grf::causal_forest(X, Y, W) scores <- double_robust_scores(c.forest) 

policytree documentation built on July 7, 2021, 9:06 a.m.