PPI++ OLS (Point Estimate)

Helper function for PPI++ OLS estimation (point estimate)

Usage

ppi_plusplus_ols_est(
  X_l,
  Y_l,
  f_l,
  X_u,
  f_u,
  lhat = NULL,
  coord = NULL,
  w_l = NULL,
  w_u = NULL
)

Arguments

X_l

(matrix): n x p matrix of covariates in the labeled data.

Y_l

(vector): n-vector of labeled outcomes.

f_l

(vector): n-vector of predictions in the labeled data.

X_u

(matrix): N x p matrix of covariates in the unlabeled data.

f_u

(vector): N-vector of predictions in the unlabeled data.

lhat

(float, optional): Power-tuning parameter (see https://arxiv.org/abs/2311.01453). The default value, NULL, will estimate the optimal value from the data. Setting lhat = 1 recovers PPI with no power tuning, and setting lhat = 0 recovers the classical point estimate.

coord

(int, optional): Coordinate for which to optimize lhat = 1. If NULL, it optimizes the total variance over all coordinates. Must be in (1, ..., d) where d is the dimension of the estimand.

w_l

(ndarray, optional): Sample weights for the labeled data set. Defaults to a vector of ones.

w_u

(ndarray, optional): Sample weights for the unlabeled data set. Defaults to a vector of ones.

Value

(vector): vector of prediction-powered point estimates of the OLS coefficients.

Details

PPI++: Efficient Prediction Powered Inference (Angelopoulos et al., 2023) https://arxiv.org/abs/2311.01453

Examples

dat <- simdat(model = "ols")

form <- Y - f ~ X1

X_l <- model.matrix(form, data = dat[dat$set == "labeled",])

Y_l <- dat[dat$set == "labeled", all.vars(form)[1]] |> matrix(ncol = 1)

f_l <- dat[dat$set == "labeled", all.vars(form)[2]] |> matrix(ncol = 1)

X_u <- model.matrix(form, data = dat[dat$set == "unlabeled",])

f_u <- dat[dat$set == "unlabeled", all.vars(form)[2]] |> matrix(ncol = 1)

ppi_plusplus_ols_est(X_l, Y_l, f_l, X_u, f_u)
#> X(Intercept)          XX1 
#>    0.7804814    1.0524179