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
Value
An object of class 'ate.targeted' is returned. See
targeted-class for more details about this class and its
generic 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, ...)
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))
#> Estimate Std.Err 2.5% 97.5% P-value
#> a=0 0.2302 0.05278 0.1268 0.3337 1.288e-05
#> a=1 0.3148 0.05466 0.2077 0.4219 8.413e-09
#> a=2 0.4961 0.04732 0.4034 0.5889 1.019e-25
#> a=3 0.6348 0.02492 0.5860 0.6836 3.667e-143
# Comparison with randomized experiment
m0 <- lava::cancel(m, a~x)
lm(y~a-1, lava::sim(m0,2e4))
#>
#> Call:
#> lm(formula = y ~ a - 1, data = lava::sim(m0, 20000))
#>
#> Coefficients:
#> a0 a1 a2 a3
#> 0.2168 0.3467 0.4051 0.6188
#>
# Choosing a different contrast for the association measures
summary(a, contrast=c(2,4))
#>
#> Augmented Inverse Probability Weighting estimator
#> Response y (Outcome model: gaussian):
#> y ~ a * x
#> Exposure a (Propensity model: logistic regression):
#> a ~ x
#>
#> Estimate Std.Err 2.5% 97.5% P-value
#> a=0 0.2302 0.05278 0.1268 0.3337 1.288e-05
#> a=1 0.3148 0.05466 0.2077 0.4219 8.413e-09
#> a=2 0.4961 0.04732 0.4034 0.5889 1.019e-25
#> a=3 0.6348 0.02492 0.5860 0.6836 3.667e-143
#>
#> Average Treatment Effect (constrast: 'a=1' - 'a=3'):
#>
#> Estimate Std.Err 2.5% 97.5% P-value
#> ATE -0.32 0.05923 -0.4361 -0.2039 6.577e-08
#>