A three-step bridge-function estimator:
Residualises X on G to isolate the U-driven component X_resid.
Regresses X_resid on the FULL W matrix to construct W_hat, a proxy for unmeasured confounding. This step requires
ncol(W) >= k(the proximal completeness condition): if W has fewer valid columns than confounders, the bridge cannot span the confounder subspace and the estimator is under-identified.Fits Y ~ X + W_hat to absorb confounding bias.
Arguments
- y
Numeric outcome vector (length n).
- X
Numeric exposure vector (length n).
- g
Numeric instrument vector (length n).
- W
Numeric negative-control matrix (n x q) or vector (length n). If a matrix, the bridge uses all q columns. Pass only validity-screened columns for the completeness condition to be meaningful.
- covars
Optional data frame of additional covariates (n rows).
Details
Unlike the scalar version (fit_pgc_scalar), which
collapses W to rowMeans(W) and is algebraically equivalent
to IV/2SLS, the matrix bridge preserves the dimensional structure
of W and is the estimator for which the completeness condition is
binding.
Examples
set.seed(1)
dat <- generate_toy_data(n = 200, seed = 1)
fit_pgc(dat$Y[, 1], dat$X, dat$G[, 1], dat$W)
#> $beta
#> [1] 0.3440353
#>
#> $se
#> [1] 0.02441775
#>
#> $pvalue
#> [1] 1.219016e-31
#>