PGC mediation estimator: bridge-function-adjusted natural effects (matrix bridge)

Extends fit_pgc (matrix bridge) to the mediation setting by constructing a confounding proxy \(\hat W\) from the full W matrix and including it in both the mediator and outcome regressions.

Usage

fit_pgc_mediation(y, X, M, g, W, covars = NULL)

Arguments

y

Numeric outcome vector (length n).

X

Numeric exposure vector (length n).

M

Numeric mediator 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.

covars

Optional data frame of additional covariates (n rows).

Value

Named list: NDE, NDE_se, NDE_p, NIE, NIE_se, NIE_p.

Details

Steps:

1. Residualise X on G -> X_resid (U-driven residual).

2. Bridge X_resid on the FULL W matrix -> W_hat (proxy for U).

3. M ~ X + W_hat -> alpha_M (adjusted for confounding proxy).

4. Y ~ X + M + W_hat -> NDE = beta_X, beta_M (adjusted).

The matrix bridge requires ncol(W) >= k (proximal completeness) for the bridge to span the confounder subspace.

Examples

set.seed(1)
dat <- generate_toy_data(n = 200, mo_confounding = 0.8, seed = 1)
fit_pgc_mediation(dat$Y[, 1], dat$X, dat$M, dat$G[, 1], dat$W)
#> $NDE
#> [1] -0.3886088
#> 
#> $NDE_se
#> [1] 0.04901454
#> 
#> $NDE_p
#> [1] 1.647096e-13
#> 
#> $NIE
#> [1] 0.7579615
#> 
#> $NIE_se
#> [1] 0.05033667
#> 
#> $NIE_p
#> [1] 3.066427e-51
#> 
#> $alpha_M
#> [1] 0.5826071
#> 
#> $alpha_se
#> [1] 0.01642378
#> 
#> $beta_M
#> [1] 1.300982
#> 
#> $beta_M_se
#> [1] 0.07822876
#>