Outcome Weights

This R package calculates the outcome weights of Knaus (2024). Its use is illustrated in the average effects R notebook and the heterogeneous effects R notebook as supplementary material to the paper.

The core functionality is the get_outcome_weights() method that implements the theoretical result in Proposition 1 showing that the outcome weights vector can be obtained in the general form \(\boldsymbol{\omega'} = (\boldsymbol{\tilde{Z}'\tilde{D}})^{-1} \boldsymbol{\tilde{Z}'T}\) where \(\boldsymbol{\tilde{Z}}\), \(\boldsymbol{\tilde{D}}\) and \(\boldsymbol{T}\) are pseudo-instrument, pseudo-treatment and the transformation matrix, respectively.

In the future it should be compatible with as many estimated R objects as possible.

The package is work in progress with the current state (suggestions welcome):

In progress

• Compatibility with grf package
  • causal_forest() outcome weights for CATE
  • instrumental_forest() outcome weights CLATE
  • causal_forest() outcome weights for ATE from average_treatment_effect()
  • All outcome weights for average parameters compatible with average_treatment_effect()
• Package internal Double ML implementation handling the required outcome smoother matrices
  • Nuisance parameter estimation based on honest random forest (regression_forest() of grf package)
  • dml_with_smoother() function runs for PLR, PLR-IV, AIPW-ATE, and Wald_AIPW and is compatible with get_outcome_weights()
  • Add more Double ML estimators
  • Add support for more smoothers

Envisioned features

• Compatibility with DoubleML (this is a non-trivial task as the mlr3 environment it builds on does not provide smoother matrices)
  • Extract the smoother matrices of mlr3 available, where possible
  • Make the smoother matrices of mlr3 accessible within DoubleML
  • Write get_outcome_weights() method for DoubleML estimators
• Collect packages where weights could be extracted and implement them

The package can be installed via devtools and soon will be available via CRAN:

library(devtools)
install_github(repo="MCKnaus/OutcomeWeights")

The following code creates synthetic data to showcase how causal forest weights are extracted and that they perfectly replicate the original output:

# Sample from DGP borrowed from grf documentation
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)

# Run outcome regression and extract smoother matrix
forest.Y = grf::regression_forest(X, Y)
Y.hat = predict(forest.Y)$predictions
outcome_smoother = grf::get_forest_weights(forest.Y)

# Run causal forest with external Y.hats
c.forest = grf::causal_forest(X, Y, W, Y.hat = Y.hat)

# Predict on out-of-bag training samples.
cate.oob = predict(c.forest)$predictions

# Predict using the forest.
X.test = matrix(0, 101, p)
X.test[, 1] = seq(-2, 2, length.out = 101)
cate.test = predict(c.forest, X.test)$predictions

# Calculate outcome weights
omega_oob = get_outcome_weights(c.forest,S = outcome_smoother)
omega_test = get_outcome_weights(c.forest,S = outcome_smoother,newdata = X.test)

# Observe that they perfectly replicate the original CATEs
all.equal(as.numeric(omega_oob$omega %*% Y), 
          as.numeric(cate.oob))
all.equal(as.numeric(omega_test$omega %*% Y), 
          as.numeric(cate.test))

# Also the ATE estimates are prefectly replicated
omega_ate = get_outcome_weights(c.forest,target = "ATE", S = outcome_smoother,S.tau = omega_oob$omega)
all.equal(as.numeric(omega_ate$omega %*% Y),
          as.numeric(grf::average_treatment_effect(c.forest, target.sample = "all")[1]))

References

Knaus, M. C. (2024). Treatment effect estimators as weighted outcomes, soon on arXiv