Estimates the average treatment effect and its exact decomposition into
a discrete-component contribution (through the boundary probabilities)
and a continuous-component contribution (through the conditional mean),
Proposition 2.3 (one boundary) / Proposition 2.4 (two boundaries) of
Ospina (2026). Identification rests on the ordinary potential-outcomes
assumptions (SUTVA, ignorability given the covariates in fit,
positivity); this function does not check them.
Arguments
- fit
A fitted model from
bic_fit().- treat
Character, the name of the treatment variable.
- data
The data frame the effect is averaged over (by default, the data
fitwas fitted on).- weights
Optional averaging weights (e.g. survey weights), normalized internally to sum to one. Defaults to equal weights.
Value
A named numeric vector c(tau, tau_alpha, tau_mu), with
tau_alpha + tau_mu == tau exactly (to floating-point precision).
Details
Reading the three numbers: tau is the total change in the mean
response caused by treatment. tau_alpha is the part of that change
coming from treatment moving units onto or off the boundary (a change
in how many units attain the inflated value); tau_mu is the part
coming from treatment shifting the conditional mean among units that
remain in the interior. They can have the same sign (both mechanisms
reinforcing) or opposite signs (one mechanism offsetting the other, so
that tau alone understates how much is actually happening); only the
three-number decomposition distinguishes these cases, since tau by
itself looks the same either way when the components happen to be
small, and looks deceptively modest when they are large and opposed.
Examples
dat <- simulate_bic(400, seed = 1)
fit <- bic_fit(y ~ T + W2, nu.formula = ~ T + W1, data = dat)
bic_gcomp(fit, "T", dat)
#> tau tau_alpha tau_mu
#> 0.04459171 -0.07564943 0.12024114
attr(dat, "truth")
#> $tau
#> [1] 0.04490327
#>
#> $tau_alpha
#> [1] -0.08649041
#>
#> $tau_mu
#> [1] 0.1313937
#>