Skip to contents

Data Generating Process with a Gaussian Covariate

Source: R/DGP_X.R
DGP_X_Gaussian.Rd

This function generates potential outcomes from a data generating process similar to the one described in Parast et al. (2024) , but with the addition of a Gaussian covariate X. It creates a dataset of potential outcomes $$P = (Y_1, S_1, Y_0, S_0)$$ and observed outcomes $$P_{observed} = (Y, S)$$ based on a random treatment assignment \(Z\).

Usage

DGP_X_Gaussian(n, p, beta, Sigma, m, s)

Arguments

n

Integer. Total sample size.

p

Numeric. Probability of being assigned to the treatment group \((Z=1)\).

beta

Numeric vector. Coefficients for the linear function of the covariate \(X\).

Sigma

Matrix. Covariance matrix for the potential outcomes.

m

Numeric. Mean of the Gaussian covariate \(X\).

s

Numeric. Standard deviation of the Gaussian covariate \(X\).

Value

A list containing:

  • X: The Gaussian covariate vector.

  • Z: Treatment assignment vector.

  • n1: Number of treated units.

  • n0: Number of control units.

  • P: Full matrix of potential outcomes.

  • P_observed: Observed outcomes \((Y, S)\) corresponding to the assigned treatment \(Z\).

  • P_unobserved: Counterfactual outcomes under the opposite treatment.

This function is useful for generating synthetic data to test or explore the method, for instance to verify the behavior of BSET_X under known simulation settings.

Details

The potential outcomes are generated from a multivariate normal distribution with mean vector and covariance matrix that depend on the value of \(X\). Specifically, the mean vector is a linear function of \(X\): $$\mu(X) = x \cdot (\beta_{Y1}, \beta_{S1}, \beta_{Y0}, \beta_{S0})^T,$$ and the covariance matrix is constant across values of \(X\): $$\Sigma(X) = \Sigma.$$

References

Carlotti P, Parast L (2026). “A Bayesian Critique of Rank-Based Methods for Surrogate Marker Evaluation.” arXiv preprint arXiv:2603.14381.

Examples

set.seed(123)
data <- DGP_X_Gaussian(
  n = 100,
  p = 0.5,
  beta = c(1, 7, 0, 6),
  Sigma = 0.5 * diag(4),
  m = 3,
  s = 1
)