R: Estimate the best linear projection of a conditional average...

best_linear_projection {grf} | R Documentation

## Estimate the best linear projection of a conditional average treatment effect using a causal forest.

### Description

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

### Usage

    best_linear_projection(
      forest,
      A = NULL,
      subset = NULL,
      debiasing.weights = NULL,
      num.trees.for.variance = 500
    )

### Arguments

`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.
`debiasing.weights` | A vector of length n (or the subset length) of debiasing weights. If NULL (default) and the treatment is binary, then inverse-propensity weighting is used, otherwise, if the treatment is continuous, these are estimated by a variance forest.
`num.trees.for.variance` | Number of trees used to estimate Var[Wi | Xi = x]. Default is 500. (only applies with continuous treatment and debiasing.weights = NULL)

### Details

tau(Xi) ~ beta_0 + Ai * beta

Procedurally, we do so by 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 distinct The case of the null model tau(Xi) ~ beta_0 is equivalent to fitting an average treatment effect via AIPW.

In the event the treatment is continuous the inverse-propensity weight component of the double robust scores are replaced with a component based on a forest based estimate of Var[Wi | Xi = x]. These weights can also be passed manually by specifying debiasing.weights.

### Value

An estimate of the best linear projection, along with coefficient standard errors.

### References

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).

### Examples

    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])

[Package grf version 1.2.0 Index]