ate {targeted}

AIPW (doubly-robust) estimator for Average Treatement 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 misspecified (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,
  ...
)

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

If TRUE all standard errors are calculated (default TRUE when exposure only has two levels)

labels

Optional treatment labels

...

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

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

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