ate: AIPW (doubly-robust) estimator for Average Treatment Effect

In targeted: Targeted Inference

AIPW (doubly-robust) estimator for Average Treatment Effect

Description

Augmented Inverse Probability Weighting estimator for the Average (Causal) Treatment Effect. All nuisance models are here parametric (glm). For a more general approach see the cate implementation. In this implementation the standard errors are correct even when the nuisance models are mis-specified (the influence curve is calculated including the term coming from the parametric nuisance models). The estimate is consistent if either the propensity model or the outcome model / Q-model is correctly specified.

Usage

ate(
  formula,
  data = parent.frame(),
  weights,
  offset,
  family = stats::gaussian(identity),
  nuisance = NULL,
  propensity = nuisance,
  all,
  labels = NULL,
  adjust.nuisance = TRUE,
  adjust.propensity = TRUE,
  ...
)

Arguments

formula	formula (see details below)
data	data.frame
weights	optional frequency weights
offset	optional offset (character or vector). can also be specified in the formula.
family	Exponential family argument for outcome model
nuisance	outcome regression formula (Q-model)
propensity	propensity model formula
all	when TRUE all standard errors are calculated (default TRUE when exposure only has two levels)
labels	optional treatment labels
adjust.nuisance	adjust for uncertainty due to estimation of outcome regression model parameters
adjust.propensity	adjust for uncertainty due to estimation of propensity regression model parameters
...	additional arguments to lower level functions

Details

The formula may either be specified as: response ~ treatment | nuisance-formula | propensity-formula

For example: ate(y~a | x+z+a | x*z, data=...)

Alternatively, as a list: ate(list(y~a, ~x+z, ~x*z), data=...)

Or using the nuisance (and propensity argument): ate(y~a, nuisance=~x+z, ...)

Value

An object of class 'ate.targeted' is returned. See targeted-class for more details about this class and its generic functions.

Author(s)

Klaus K. Holst

See Also

cate

Examples

m <- lava::lvm(y ~ a+x, a~x) |>
     lava::distribution(~y, value = lava::binomial.lvm()) |>
     lava::ordinal(K=4, ~a) |>
     transform(~a, value = factor)
d <- lava::sim(m, 1e3, seed=1)
# (a <- ate(y~a|a*x|x, data=d))
(a <- ate(y~a, nuisance=~a*x, propensity=~x, data = d))

# Comparison with randomized experiment
m0 <- lava::cancel(m, a~x)
lm(y~a-1, lava::sim(m0,2e4))

# Choosing a different contrast for the association measures
summary(a, contrast=c(2,4))

targeted documentation built on Jan. 12, 2026, 9:08 a.m.