Skip to contents

Power curve for PPI mean with supplied population moments

power_curve_mean_dgp.Rd

Computes analytical and Monte Carlo power for the prediction-powered mean estimator across a grid of labeled sample sizes n_grid, given population moments and an effect size. This function does not simulate a superpopulation; instead, you provide the required moments: \(\sigma_f^2 = Var(f(X))\), \(\sigma_{\mathrm{res}}^2 = Var(Y - f(X))\), and the effect size \(\delta = \theta - \theta_0\). For each n in n_grid, analytical power is computed from the normal theory formula using \(\sqrt{\sigma_f^2/N + \sigma_{\mathrm{res}}^2/n}\), and empirical power is estimated via Monte Carlo using simulate_ppi_vanilla_mean().

Usage

power_curve_mean_dgp(
  n_grid = seq(50, 200, by = 25),
  N,
  theta0 = 0,
  var_f = 0.45,
  var_res = 0.8,
  delta = 0.2,
  family = stats::gaussian(),
  R = 1000,
  alpha = 0.05,
  seed = 1
)

Arguments

n_grid

Numeric vector of labeled sample sizes to evaluate.

N

Unlabeled sample size.

theta0

Null value for the mean estimand \(\theta_0\).

var_f

Population variance of predictions \(Var(f(X))\).

var_res

Population residual variance \(Var(Y - f(X))\).

delta

Effect size \(\theta - \theta_0\).

family

GLM family (default stats::gaussian()). Included for API consistency; the analytical calculation depends only on var_f, var_res, N, n, and delta.

R

Number of Monte Carlo replicates for empirical power (default 1000).

alpha

Two-sided test level (default 0.05).

seed

RNG seed used inside the per-n simulations.

Value

A data frame with one row per n in n_grid, containing:

n

Labeled sample size.

analytical

Analytical power from the normal theory formula.

empirical

Monte Carlo power (rejection rate).

abs_diff

Absolute difference |empirical - analytical|.

Examples

power_curve_mean_dgp(
  n_grid = seq(50, 200, by = 25),
  N = 3000,
  theta0 = 0,
  var_f = 0.45,
  var_res = 0.80,
  delta = 0.2,
  R = 1000
)
#>     n analytical empirical     abs_diff
#> 1  50  0.3498847     0.373 0.0231153218
#> 2  75  0.4853155     0.510 0.0246845069
#> 3 100  0.6008198     0.582 0.0188198063
#> 4 125  0.6954147     0.696 0.0005853261
#> 5 150  0.7706339     0.754 0.0166338854
#> 6 175  0.8291243     0.836 0.0068757262
#> 7 200  0.8738207     0.871 0.0028206571