Augmented inverse-probability-weighted (doubly robust) ATE

tau = mean(m1 - m0 + T(y - m1)/e - (1-T)(y - m0)/(1-e)).

Usage

morie_caus_aipw(y, T, ps, m1, m0, trim = 0.01)

Arguments

y: observed outcome.
T: binary treatment.
ps: estimated propensity score.
m1, m0: estimated outcome regressions for every unit.
trim: propensities are clipped to [trim, 1 - trim].

Value

list: ate, se, ci, influence, regression_component, augmentation_component, n_trimmed, min_ps, max_ps, effective_overlap, n, method.

Details

The DOUBLE ROBUSTNESS is the property worth having: consistent if EITHER the propensity score or the outcome regressions are correctly specified, not necessarily both. Get both wrong and it is wrong, and no amount of doubly robust machinery rescues that.

If m is right the augmentation terms have mean zero and this is the regression estimator; if e is right the terms rearrange into inverse-probability weighting with the regression as a control.

Propensities near 0 or 1 are the practical failure mode, since the estimator divides by them. trim bounds them and n_trimmed reports how many were touched, because trimming changes the estimand to an average over the retained region.

References

Robins, Rotnitzky and Zhao (1994), JASA 89:846-866; Bang and Robins (2005), Biometrics 61:962-973.

Examples

set.seed(1)
n <- 200
e <- rep(0.5, n)
T <- stats::rbinom(n, 1, e)
m0 <- stats::rnorm(n)
morie_caus_aipw(m0 + 2 * T, T, e, m0 + 2, m0)$ate
#> [1] 2