PGC estimator: Proxy G-Component Correction (scalar bridge)

The original ICONIC PGC implementation, which summarises the negative-control panel as a scalar (rowMeans(W)) before bridging. This version is numerically stable and works in small samples, but the scalar bridge produces \(\hat W\) proportional to the G-residualised exposure by construction, making the estimator algebraically equivalent to IV/2SLS when the instrument is valid. The proximal completeness condition (dim(W_valid) >= k) is NOT binding for this estimator.

Usage

fit_pgc_scalar(y, X, g, w, covars = NULL)

Arguments

y

Numeric outcome vector (length n).

X

Numeric exposure vector (length n).

g

Numeric instrument vector (length n).

w

Numeric negative-control vector (length n). Pass rowMeans(W_matrix) for stability.

covars

Optional data frame of additional covariates (n rows).

Value

Named list: beta, se, pvalue.

Details

Use fit_pgc (matrix bridge) when the completeness condition is of interest. Use this function as a stable fallback when n is small relative to the number of valid controls, or as an IV-equivalent benchmark.

Examples

set.seed(1)
dat <- generate_toy_data(n = 200, seed = 1)
fit_pgc_scalar(dat$Y[, 1], dat$X, dat$G[, 1], rowMeans(dat$W))
#> $beta
#> [1] 0.2989159
#> 
#> $se
#> [1] 0.03344448
#> 
#> $pvalue
#> [1] 2.869071e-16
#>