targeted (version 0.6)

ate: 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,
  ...
)

Value

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

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

Author

Klaus K. Holst

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, ...)

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))