Nonlinear heteroskedastic synthetic DGP for CausalStress (v1.3.0) — dgp_synth_nonlinear_heteroskedastic

Implements the synth_nonlinear_heteroskedastic design from the DGP registry. This DGP has nonlinear baseline outcome, constant treatment effect, and heteroskedastic Gaussian noise.

Usage

dgp_synth_nonlinear_heteroskedastic_v130(
  n,
  seed = NULL,
  include_truth = TRUE,
  oracle_only = FALSE
)

Arguments

n: Integer, number of observations.
seed: Optional seed for reproducibility (passed to cs_set_rng()).
include_truth: Logical; if TRUE, include oracle truth tables where supported.
oracle_only: Logical; if TRUE, return only columns needed for oracle truth generation where supported.

Value

A list with df, true_att, true_qst, and meta satisfying the synthetic DGP contract.

Details

Goal: Test curve fitting and variance adaptation.

Covariates: \(X \in \mathbb{R}^4\).

\(X_1, X_2 \sim \mathcal{N}(0,1)\).
\(X_3 \sim \mathcal{U}[-2, 2]\).
\(X_4 \sim \mathrm{Bernoulli}(0.4)\).

Outcome: \(Y_0 = 1 + 0.8 \sin(X_1) + 0.5 X_2^2 - 0.3 X_4\).

Treatment effect: \(\tau(X) = 1.0\) (constant).

Noise: Gaussian with heteroskedastic scale \(\varepsilon \sim \mathcal{N}(0, \sigma(X)^2)\) where \(\sigma(X) = 0.3 + 0.2 |X_3|\).

Propensity: \(p(X) = \mathrm{plogis}(0.5 X_1 - 0.5 X_2)\).