Overlap-weighted doubly-robust ATE with cross-fitting

The augmented-IPW score, weighted by \(e(1-e)\) and fitted with cross-fitting so that no observation contributes to the nuisance models used to score it.

Usage

morie_dr_overlap_weighted(y, D, X, ps = NULL, n_folds = 2, seed = 0)

Arguments

y

outcome.

D

0/1 treatment.

X

covariates.

ps

optional externally supplied propensity scores.

n_folds

cross-fitting folds, at least 2.

seed

integer seed for the fold assignment.

Value

list with ate, se, ci, estimand, influence, propensity, mu1, mu0.

Details

"Doubly robust" means consistent if EITHER the propensity model or the outcome model is correct. It does not mean the estimator survives both being wrong, which is how the term is often used in practice.

Cross-fitting is not optional here. Without it the nuisance estimates are correlated with the residuals they are supposed to be orthogonal to, and the standard error is understated by an amount that grows with model flexibility.

The overlap weights keep the \(1/e\) factor from exploding near the boundary, at the cost of estimating the effect for the overlap population rather than the full one – the returned estimand says so.

References

Chernozhukov, V. et al. (2018). Double/debiased machine learning. The Econometrics Journal, 21(1), C1-C68. Li, F. et al. (2018). Balancing covariates via propensity score weighting. JASA, 113(521), 390-400.

Examples

set.seed(1)
X <- matrix(rnorm(400), ncol = 2)
D <- rbinom(200, 1, plogis(X[, 1]))
y <- X[, 1] + 2 * D + rnorm(200)
round(morie_dr_overlap_weighted(y, D, X)$ate, 2)
#> [1] 2.1