| best_linear_projection {grf} | R Documentation |
Let tau(Xi) = E[Y(1) - Y(0) | X = Xi] be the CATE, and Ai be a vector of user-provided covariates. This function provides a (doubly robust) fit to the linear model
best_linear_projection(forest, A = NULL, subset = NULL)
forest |
The trained forest. |
A |
The covariates we want to project the CATE onto. |
subset |
Specifies subset of the training examples over which we estimate the ATE. WARNING: For valid statistical performance, the subset should be defined only using features Xi, not using the treatment Wi or the outcome Yi. |
tau(Xi) ~ beta_0 + Ai * beta
Procedurally, we do so be regressing doubly robust scores derived from the causal forest against the Ai. Note the covariates Ai may consist of a subset of the Xi, or they may be distince The case of the null model tau(Xi) ~ beta_0 is equivalent to fitting an average treatment effect via AIPW.
An estimate of the best linear projection, along with coefficient standard errors.
Chernozhukov, Victor, and Vira Semenova. "Simultaneous inference for Best Linear Predictor of the Conditional Average Treatment Effect and other structural functions." arXiv preprint arXiv:1702.06240 (2017).
## Not run: n <- 800 p <- 5 X <- matrix(rnorm(n * p), n, p) W <- rbinom(n, 1, 0.25 + 0.5 * (X[, 1] > 0)) Y <- pmax(X[, 1], 0) * W + X[, 2] + pmin(X[, 3], 0) + rnorm(n) forest <- causal_forest(X, Y, W) best_linear_projection(forest, X[,1:2]) ## End(Not run)