Kang-Schafer placebo synthetic DGP (sharp null, v1.4.0) — dgp_synth_placebo_kangschafer

Implements the synth_placebo_kangschafer design: latent Gaussian covariates transformed nonlinearly to observed X, linear outcome/propensity in latent Z, and sharp-null treatment effect (Y1 == Y0 pathwise).

Usage

dgp_synth_placebo_kangschafer_v140(
  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 synthetic DGP list with df, true_att, true_qst, meta.

Details

Goal: Canonical misspecification trap (Kang–Schafer) adapted as a sharp-null placebo; any nonzero effect indicates functional-form failure.

Description: Data are generated from latent Gaussian covariates $Z$, but the analyst only observes nonlinear transforms $X = f(Z)$. True outcome regression and propensity are linear in $Z$ yet become severely misspecified when fit linearly in the observed $X$. Treatment effect is zero pathwise.

Generative structure:

Latent covariates (unobserved): $Z = (Z_1, Z_2, Z_3, Z_4)^\top \sim \mathcal{N}_4(0, I_4)$.
Observed covariates (returned): $$X_1 = \exp(Z_1/2),\quad X_2 = \frac{Z_2}{1 + \exp(Z_1)} + 10,$$ $$X_3 = (Z_1 Z_3 / 25 + 0.6)^3,\quad X_4 = (Z_2 + Z_4 + 20)^2.$$
Propensity (in $Z$): $p(Z) = \mathrm{expit}(-Z_1 + 0.5 Z_2 - 0.25 Z_3 - 0.1 Z_4)$, with $W \sim \mathrm{Bernoulli}(p(Z))$.
Baseline outcome (in $Z$): $$\mu_0(Z) = 210 + 27.4 Z_1 + 13.7 Z_2 + 13.7 Z_3 + 13.7 Z_4,$$ $Y_0 = \mu_0(Z) + \varepsilon$, $\varepsilon \sim \mathcal{N}(0,1)$.
Treatment effect (sharp null): $\tau(Z) \equiv 0$, so $Y_1 = Y_0$ and $Y = Y_0$.

Returned fields: df contains y, w, y0, y1, p, structural_te, X1–X4; structural_te is all zeros; true_att = 0; true_qst is identically zero on cs_tau_oracle().

Challenge: Severe outcome and propensity misspecification in observed $X$-space; belongs in the placebo suite.