High-dimensional sparse partially linear DGP (v1.3.0) — dgp_synth_hd_sparse_plm

Implements the synth_hd_sparse_plm design from the DGP registry 1.3.0: correlated Gaussian covariates (p = 50) with sparse linear outcome and propensity, constant ATT tau = 1.

Usage

dgp_synth_hd_sparse_plm_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 synthetic DGP list with df, true_att, true_qst, and meta.

Details

Goal: High-dimensional sparse nuisance setting for modern ML estimators (DML, R-learner, causal forests, GenGC).

Description: Partially linear model with \(X \in \mathbb{R}^{50}\), sparse linear outcome regression and sparse logistic propensity, constant treatment effect. Covariates follow a Toeplitz correlation to induce regularization difficulty.

Generative structure:

Covariates: \(X \sim \mathcal{N}(0, \Sigma)\) with \(\Sigma_{ij} = 0.5^{|i-j|}\), returned as X1–X50.
Outcome regression (sparse): \(\beta^{(Y)}_1 = \dots = \beta^{(Y)}_5 = 1\), others zero; \(\mu_0(X) = X^\top \beta^{(Y)}\), \(Y_0 = \mu_0(X) + \varepsilon\), \(\varepsilon \sim \mathcal{N}(0,1)\).
Treatment effect: \(\tau(X) \equiv 1.0\), so \(Y_1 = Y_0 + 1\).
Propensity (sparse): \(\gamma = (0.5, -0.5, 0.25, -0.25, 0.1, 0,\dots,0)\), \(p(X) = \mathrm{expit}(X^\top \gamma)\), \(W \sim \mathrm{Bernoulli}(p(X))\).

Returned fields: df includes y, w, y0, y1, p, structural_te, and X1–X50; structural_te is all ones; true_att = 1.0; true_qst reflects a constant +1 shift on the cs_tau_oracle() grid.

Challenge: Correlated, high-dimensional sparse nuisance learning; tests variable selection, regularization bias, and orthogonalization robustness.