PGC binary mediation estimator: single-panel bridge with logistic / LPM

Bridge-function-adjusted natural direct and indirect effects with a binary outcome stage, using a single negative-control panel W for both the X->M and M->Y confounding paths. This is the binary analogue of fit_pgc_mediation (continuous outcome):

1. OLS: residualise X on G -> X_resid.

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

3. OLS: M ~ X + W_hat + covars -> alpha_M.

4. Logistic / LPM: y ~ X + M + W_hat + covars -> NDE (coef on X), beta_M (coef on M).

NIE = alpha_M * beta_M. Unlike fit_pgc_mediation2_bin, which uses path-specific W1/W2 bridges, this estimator uses a single combined W panel and is appropriate when separate conf_XM / conf_MY confounders are not assumed.

Usage

fit_pgc_mediation_bin(
  y,
  X,
  M,
  g,
  W,
  covars = NULL,
  min_f = 10,
  effect_scale = c("logor", "riskdiff")
)

Arguments

y

Numeric 0/1 outcome vector (length n).

X

Numeric exposure vector (length n).

M

Numeric mediator vector (length n).

g

Numeric instrument for X (length n).

W

Numeric NC matrix (n x q) or vector (length n).

covars

Optional data frame of covariates (n rows).

min_f

Minimum partial F for G. Default 10.

effect_scale

Character: "logor" or "riskdiff".

Value

Named list (same fields as fit_unadj_mediation_bin).

Examples

set.seed(1)
dat <- generate_toy_data(n = 500, outcome_type = "binary",
mo_confounding = 0.8, seed = 1)
fit_pgc_mediation_bin(dat$y_bin, dat$X, dat$M, dat$G[, 1], dat$W)
#> $NDE
#> [1] -0.5448331
#> 
#> $NDE_se
#> [1] 0.3615117
#> 
#> $NDE_p
#> [1] 0.1317858
#> 
#> $NIE
#> [1] 0.985109
#> 
#> $NIE_se
#> [1] 0.3428178
#> 
#> $NIE_p
#> [1] 0.004058685
#> 
#> $alpha_M
#> [1] 0.5912409
#> 
#> $alpha_se
#> [1] 0.01002849
#> 
#> $beta_M
#> [1] 1.666172
#> 
#> $beta_M_se
#> [1] 0.5791386
#>