Doubly Robust Distributional Effect on the Treated Test (DR-DETT)

Tests whether the distribution of the treated potential outcome Y(1) differs from the control potential outcome Y(0) among the treated subpopulation. Requires only one-sided overlap.

Usage

dr_dett_test(
  y,
  treatment,
  covariates,
  kernel_y = kernel_spec(),
  propensity_model = c("logistic", "ranger", "xgboost"),
  outcome_model = c("krr", "zero"),
  cross_fit = TRUE,
  n_folds = 5L,
  n_permutations = 500L,
  n_bins = 10L,
  regularisation = "cv",
  min_ess_fraction = 0.1,
  alpha = 0.05,
  seed = NULL,
  verbose = FALSE
)

Arguments

y: Numeric vector or matrix. Outcome variable.
treatment: Binary vector (0/1). Treatment indicator.
covariates: Numeric matrix, data.frame, or data.table. Confounders.
kernel_y: Kernel specification for outcome space. Default is RBF.
propensity_model: Character. Method for propensity estimation: "logistic" (default), "ranger", or "xgboost".
outcome_model: Character. "krr" (kernel ridge regression, default) fits a conditional mean embedding for each arm and forms the doubly robust statistic; "zero" drops the outcome model and returns the inverse-probability-weighted (singly robust) statistic.
cross_fit: Logical. If TRUE (default), both nuisances – the propensity score and the conditional mean embedding – are estimated by n_folds-fold cross-fitting and evaluated out-of-fold, as the doubly robust theory requires under flexible nuisance estimators. If FALSE, both are fit in-sample (faster, but the test can be anti-conservative).
n_folds: Integer. Number of cross-fitting folds. Default is 5.
n_permutations: Integer. Number of permutations. Default is 500.
n_bins: Integer. Propensity score bins for permutation. Default is 10.
regularisation: Numeric or "cv". Ridge parameter for the CME. Default is "cv".
min_ess_fraction: Numeric in (0, 1). If the effective sample size of either arm's inverse-probability weights falls below this fraction of n, a reliability warning() is emitted. Default 0.1.
alpha: Numeric. Significance level. Default is 0.05.
seed: Integer or NULL. Random seed. Permutations are drawn through R's RNG, so a fixed seed makes the test fully reproducible.
verbose: Logical. Print progress. Default is FALSE.

Value

An object of class "kernel_test_result". The ess element holds the effective sample size of the control reconstruction weights and ess_warning records whether the reliability floor was hit.

Details

DR-DETT is analogous to DR-DATE but focuses on the effect on the treated (ETT) rather than the average treatment effect. The treated counterfactual Y(1) | T = 1 is observed directly, so only the control arm needs an outcome model. The control counterfactual Y(0) | T = 1 is reconstructed by augmented inverse-probability weighting, reweighting controls by the treatment odds \(e(x) / (1 - e(x))\) so that their covariate distribution matches the treated. With outcome_model = "krr" the control conditional mean embedding \(\hat m_0\) supplies the doubly robust augmentation; outcome_model = "zero" returns the inverse-probability-weighted statistic. It requires only one-sided overlap: P(T = 1 | X) bounded away from 0 (not necessarily from 1), so it applies where positivity fails for the control group.

References

Fawkes, J., Hu, R., Evans, R. J., & Sejdinovic, D. (2024). Doubly robust kernel statistics for testing distributional treatment effects. Transactions on Machine Learning Research.

Examples

set.seed(42)
n <- 300
x <- matrix(rnorm(n * 2), n, 2)
t <- rbinom(n, 1, plogis(0.5 * x[, 1]))
y <- t * rnorm(n, sd = 2) + (1 - t) * rnorm(n, sd = 1) + x[, 1]

result <- dr_dett_test(y, t, x, n_permutations = 200, seed = 1)
print(result)
#> 
#>    DR-DETT Test
#> 
#> Statistic: 0.0342116 
#> P-value:   0.0149 
#> N:         300 
#> Perms:     200 
#> Kernel Y:  rbf (bw = 1.716)
#> ESS:       102.2 
#>