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Draw one sample from a named CATE simulation DGP

Source: R/sim-cate-data.R
sim_cate_data.Rd

Generates a synthetic dataset for the CATE simulation study, including oracle nuisance quantities \(e\), \(m_0\), \(m_1\), the AIPW score used by the general DNN CATE benchmarks, and the Robinson pseudo-outcome \(\rho\) used by the Robinson-style estimator route.

Usage

sim_cate_data(
  design,
  n,
  kx = 2L,
  sigma = 0.5,
  clip = 0.001,
  seed = NULL,
  x0 = NULL,
  ...
)

Arguments

design

Character; one of "dgp1_linear", "dgp2_nonlinear", "dgp3_sparse_overlap", "dgp4_clustered", "dgp5_correlated", or "dgp6_nuisance_efficiency".

n

Integer sample size.

kx

Integer covariate dimension (must be \(\ge 2\)).

sigma

Noise standard deviation in \(Y\).

clip

Propensity clipping bound in \((0, 0.5)\).

seed

Optional integer seed for reproducibility.

x0

Optional numeric length-kx evaluation point. Defaults are DGP-specific interior points: \((0,\ldots,0)\) for dgp1_linear, \((1,0,\ldots)\) for dgp2_nonlinear, dgp3_sparse_overlap, and dgp4_clustered, and dgp6_nuisance_efficiency, and \((0.75,0,\ldots)\) for dgp5_correlated.

...

Extra arguments forwarded to the underlying DGP (e.g. r and c_sharp for dgp3_sparse_overlap).

Value

A list with:

  • data: a data.frame with columns X1..Xkx, D, Y, and oracle nuisances e_oracle, m_oracle, m0_oracle, m1_oracle, tau_oracle, aipw_oracle, and the Robinson pseudo-outcome rho_oracle.

  • x0: numeric length-kx evaluation point.

  • tau_x0: true treatment effect at x0.

  • truth: named list of closures tau_fn, e_fn, m0_fn, m_fn.

Details

Six designs are available:

dgp1_linear

Linear CATE \(\tau(x) = \beta'x\); logistic propensity. Correctly specified for the OLS-interaction benchmark.

dgp2_nonlinear

Sharpened nonlinear CATE \(\tau(x) = 0.5 + 0.75\sin(1.5 x_1)\); same propensity. Misspecified for OLS; primary horse-race DGP. Default target is the interior point \(x_0 = (1,0,\ldots)\) so the local CATE is visibly nonlinear around the evaluation point.

dgp3_sparse_overlap

Same \(\tau\) as DGP 2; propensity interpolates between 0.5 at x0 and a much sharper near-boundary logistic far from x0, using a tighter Gaussian overlap pocket. Tests estimators that do not adapt to local effective sample size. Default target is the same interior point \(x_0 = (1,0,\ldots)\).

dgp4_clustered

Same \(\tau\) and propensity as DGP 2; covariates from a three-component mixture: 80\ x0) plus two diffuse 10\ \((4.5,2,0,\ldots)\) and \((-2.5,-2,0,\ldots)\) with covariance \(1.25^2 I\). Tests density adaptivity: the DNN s-NN bandwidth automatically shrinks at the dense x0, while a fixed-bandwidth kernel over-smooths. Default target is the interior point \(x_0 = (1,0,\ldots)\) and the inner cluster is recentered there.

dgp5_correlated

Covariates \(X \sim N(0,\Sigma)\) with \(\Sigma_{12} = \rho = 0.85\); \(\tau(x) = \sin(2x_1) + 0.5x_1^2\); evaluation point at \(x_0 = (0.75, 0)\). Tests shape adaptivity: L2 and diagonal-scaled neighbourhoods are misaligned with the elliptical covariate isocontours; the dnn_oracle_mahal benchmark (Mahalanobis distance) corrects for the off-diagonal covariance.

dgp6_nuisance_efficiency

Propensity \(e(x) = \operatorname{logit}^{-1}(1.25(x_1 - 1) - 0.75x_2)\) and marginal regression \(m(x) = 1 + 1.5(x_1 - 1) - x_2\) are aligned with simple benchmark nuisance models, while \(\tau(x) = 0.5 + 0.60\sin(1.5 x_1)\) remains nonlinear. Tests the precision gap between dnn_fullsample and dnn_crossfit. Default target is \(x_0 = (1,0,\ldots)\).

Examples

dgp <- sim_cate_data("dgp2_nonlinear", n = 200, kx = 2, seed = 1)
head(dgp$data)
#>           X1         X2 D          Y  e_oracle    m_oracle   m0_oracle
#> 1 -0.6264538  0.4094018 1 -0.1027314 0.3733369 -0.07525289 -0.03585565
#> 2  0.1836433  1.6888733 0 -0.6536643 0.3202518 -0.27977405 -0.50522996
#> 3 -0.8356286  1.5865884 1 -2.2263866 0.2295050 -1.47099798 -1.42221705
#> 4  1.5952808 -0.3309078 0  2.9318349 0.7237409  3.65752847  2.92618860
#> 5  0.3295078 -2.2852355 1  4.9663302 0.7870730  4.28830964  3.61474331
#> 6 -0.8204684  2.4976616 0 -1.5211462 0.1598876 -2.35123350 -2.31812997
#>    m1_oracle tau_oracle  rho_oracle  aipw_oracle
#> 1 -0.1413830 -0.1055273 -0.07360245 -0.001997335
#> 2  0.1987659  0.7039958  0.55004224  0.922362435
#> 3 -1.6347655 -0.2125485 -3.29138258 -2.790362454
#> 4  3.9366882  1.0104996  2.62685842  0.990060973
#> 5  4.4705297  0.8557864  0.86144554  1.485715869
#> 6 -2.5251725 -0.2070425 -0.98806684 -1.155705703
dgp$tau_x0
#> [1] 1.248121