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Construct Hessian/Fisher and Covariance Blocks for PPI/PPI++ Regression

compute_ppi_blocks.Rd

Computes all required Hessian/Fisher information matrices and covariance blocks used by Prediction-Powered Inference (PPI) and PPI++ for regression-based estimands (OLS or GLM contrasts).

This helper wraps:

  • compute_hessian_fisher — model Hessian or Fisher information

  • compute_sigma_blocks — Sigma-block covariance components

and produces a unified object that can be passed directly to power_ppi_regression() for labeled sample size calculations.

Usage

compute_ppi_blocks(
  model_type = c("ols", "glm"),
  X_l,
  Y_l,
  f_l,
  X_u,
  f_u,
  beta = NULL,
  family = NULL
)

Arguments

model_type

Character string: "ols" or "glm". Determines whether the estimator is linear regression (OLS) or a GLM.

X_l

Matrix of labeled covariates (n x p).

Y_l

Vector of labeled responses (required for OLS and GLM).

f_l

Vector of model predictions on labeled data.

X_u

Matrix of unlabeled covariates (N x p).

f_u

Vector of model predictions on unlabeled data.

beta

Numeric vector of regression coefficients used for Hessian/Fisher evaluation. Required for GLM; optional for OLS.

family

GLM family ("binomial" or "gaussian"). Only used for model_type = "glm".

Value

A named list of matrices:

H_L

Labeled-data Hessian / Fisher information (p x p)

H_U

Unlabeled-data Hessian / Fisher information (p x p)

Sigma_YY

Covariance of labeled score (Y - X beta) (p x p)

Sigma_ff_l

Covariance of prediction score on labeled data (p x p)

Sigma_ff_u

Covariance of prediction score on unlabeled data (p x p)

Sigma_Yf

Cross-covariance between labeled scores and prediction scores (p x p)

These matrices are exactly the inputs needed for power_ppi_regression() in type = "regression" mode.

See also

power_ppi_regression

Examples

set.seed(1)
p <- 3
n_l <- 400
n_u <- 2000

X_l <- matrix(rnorm(n_l * p), n_l, p)
X_u <- matrix(rnorm(n_u * p), n_u, p)
beta <- c(1, -0.5, 0.3)

# Labeled response and predictions
Y_l <- drop(X_l %*% beta + rnorm(n_l))
f_l <- drop(X_l %*% beta + rnorm(n_l, sd = 0.3))
f_u <- drop(X_u %*% beta + rnorm(n_u, sd = 0.3))

blocks <- compute_ppi_blocks(
  model_type = "ols",
  X_l = X_l, Y_l = Y_l, f_l = f_l,
  X_u = X_u, f_u = f_u,
  beta = beta
)

# Use in sample size solver:
c_vec <- c(1, 0, 0)
delta <- as.numeric(t(c_vec) %*% beta)

power_ppi_regression(
  delta = delta, N = n_u, power = 0.80,
  lambda_mode = "oracle",
  c = c_vec,
  H_L = blocks$H_L, H_U = blocks$H_U,
  Sigma_YY = blocks$Sigma_YY,
  Sigma_ff_l = blocks$Sigma_ff_l,
  Sigma_ff_u = blocks$Sigma_ff_u,
  Sigma_Yf = blocks$Sigma_Yf
)
#> [1] 8