Direct-proxy negative-control model

Each control is a coverage-weighted mixture of the captured confounders plus noise. With one confounder and coverage = omega this reduces to the classic w_signal proxy in generate_toy_data(). Setting captured to a strict subset of the confounders models controls that miss part of the confounder subspace (invalidating the negative-control assumption).

Usage

nc_proxy(U, covariates, params)

Arguments

U

n x k confounder matrix.

covariates

Covariate data frame (unused; kept for the NC contract).

params

List with n_features, and optionally coverage (scalar in [0, 1], default 0.7), captured (integer confounder indices the controls see, default all), noise_sd (default 0.3), MMCon (loading multiplier, default 1), mode (default "shared"), and noise_cor (a p x p correlation matrix for correlated noise, or NULL for independent noise).

Value

n x n_features matrix of negative controls.

Details

When noise_cor is supplied (a p x p correlation matrix), the noise component is drawn from a multivariate normal with that correlation structure, so the negative controls retain realistic cross-feature correlations conditional on the confounder. When noise_cor is NULL (default), the noise is independent across features.

Modes

"shared"

All columns carry the same rowMeans(U[, captured]) signal. This is the original behaviour (backward-compatible) and is numerically stable, but the W matrix has only one effective dimension regardless of n_features, so the proximal completeness condition is never binding for the matrix-bridge PGC.

"distinct"

Column f captures confounder captured[((f - 1) \%\% length(captured)) + 1]. Different columns therefore carry signals from different confounders, giving the W matrix genuine dimensional structure. This is the mode to use when benchmarking the completeness cliff: the matrix-bridge PGC is identified only when n_features >= k.

Examples

U <- matrix(rnorm(100), 100, 1)
W <- nc_proxy(U, covariates = NULL,
  params = list(n_features = 10, coverage = 0.7))
dim(W)
#> [1] 100  10