DGP Dossier: synth_overlap_stressed

1. Identity & Status

DGP ID	synth_overlap_stressed
Version	1.6.0
Status	experimental
Difficulty	★★★★☆ (4/5)
Stress Profile	overlap: severenoise: gaussianlinearity: lineareffect: lineartarget: both

2. What This DGP Stresses (Intent)

Positivity violation. The propensity is pushed toward 0/1, creating unstable inverse weights.

3. Identification Assumptions (Explicit)

• Selection on observables holds.
• Overlap is intentionally violated (severe).
• SUTVA holds.

4. Mathematical Specification

Covariates: [ X (0, I_5) ]

Propensity: [ p(X) = (9 X_1 + 9 X_2) ]

The coefficient 9.0 pushes probability mass toward 0 and 1.

Outcome (control): [ _0(X) = 1 + X_1 + 0.5 X_2 ]

Treatment effect: [ (X) = 1 + 0.5 X_1 ]

Noise: [ (0, 0.5^2) ]

5. Oracle Truth Definition

• True ATT is computed from structural_te among treated units.
• True QST is computed on the oracle tau grid (cs_get_oracle_qst()).

6. Visual Diagnostics (n = 5000)

7. Empirical Validation

IPW fails in benchmarks under this v1.6.0 hardened overlap design: weights explode and the effective sample size collapses toward 0.

Empirical validation (n=1000, seeds=1:10)

estimator_id	mean_bias	rmse
ipw_att	0.591	0.612
oracle_att	0.000	0.000

8. Failure Mode Summary

• Overlap-driven instability is primarily a variance problem (weight explosion).
• Methods need trimming/stabilization to behave well here.

9. Implementation Reference

• Generator: R/dgp-synth-overlap-stressed.R
• Registry: cs_dgp_registry() entry for synth_overlap_stressed
• Oracle truth: cs_get_oracle_qst("synth_overlap_stressed", version = "1.6.0")

10. Validation Checklist

• Propensity specified as expit(9X1 + 9X2)
• X1 vs X2 titled “Covariate Overlap (Joint Support)”
• IPW benchmark failure noted

11. Changelog

• v1.4.0: Parameter hardening (Deprecated v1.3.0).
• v1.6.0: Implemented Common Random Numbers (CRN) for Oracle generation. This reduces Monte Carlo variance of the QST contrast; it does not eliminate empirical-quantile sampling uncertainty.

Appendix: Implementation

Source code for: dgp_synth_overlap_stressed_v160

function (n, seed = NULL, include_truth = TRUE, oracle_only = FALSE) 
{
    if (!is.null(seed)) {
        cs_set_rng(seed)
    }
    X1 <- stats::rnorm(n, mean = 0, sd = 1)
    X2 <- stats::rnorm(n, mean = 0, sd = 1)
    if (!isTRUE(oracle_only)) {
        X3 <- stats::rnorm(n, mean = 0, sd = 1)
        X4 <- stats::rnorm(n, mean = 0, sd = 1)
        X5 <- stats::rnorm(n, mean = 0, sd = 1)
    }
    mu0 <- 1 + X1 + 0.5 * X2
    tau <- 1 + 0.5 * X1
    p <- stats::plogis(9 * X1 + 9 * X2)
    w <- stats::rbinom(n, size = 1L, prob = p)
    eps0 <- stats::rnorm(n, mean = 0, sd = 0.5)
    if (isTRUE(oracle_only)) {
        eps1 <- eps0
    }
    else {
        eps1 <- stats::rnorm(n, mean = 0, sd = 0.5)
    }
    y0 <- mu0 + eps0
    y1 <- mu0 + tau + eps1
    if (isTRUE(oracle_only)) {
        return(list(df = tibble::tibble(w = w, y0 = y0, y1 = y1)))
    }
    y <- ifelse(w == 1L, y1, y0)
    true_att <- cs_true_att(structural_te = tau, w = w)
    true_qst <- if (isTRUE(include_truth)) {
        cs_get_oracle_qst("synth_overlap_stressed", version = "1.6.0")
    }
    else {
        tibble::tibble(tau = cs_tau_oracle, value = rep(NA_real_, 
            length(cs_tau_oracle)))
    }
    out <- list(df = tibble::tibble(y = y, w = w, y0 = y0, y1 = y1, 
        p = p, structural_te = tau, X1 = X1, X2 = X2, X3 = X3, 
        X4 = X4, X5 = X5), true_att = true_att, true_qst = true_qst, 
        meta = list(dgp_id = "synth_overlap_stressed", version = "1.6.0", 
            type = "synthetic", params = list(n = n, seed = seed), 
            structural_te = tau))
    cs_check_dgp_synthetic(out)
    out
}
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