Doubly Robust Distributional Average Treatment Effect Test (DR-DATE)

Tests whether the distributions of potential outcomes Y(1) and Y(0) differ using a doubly robust kernel MMD statistic. Detects distributional effects (variance, shape) that mean-based tests miss.

Usage

dr_date_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 smaller of the two per-arm effective sample sizes and ess_warning records whether the reliability floor was hit.

Details

The DR-DATE test (Fawkes, Hu, Evans & Sejdinovic, 2024) constructs doubly robust (augmented inverse-probability-weighted) estimators for the counterfactual mean embeddings of Y(1) and Y(0) in a reproducing kernel Hilbert space. For arm $a$ the augmented embedding is $$\hat\mu_a = \frac{1}{n}\sum_i \tilde w_{a,i} \bigl(k(y_i,\cdot) - \hat m_a(x_i)\bigr) + \hat m_a(x_i),$$ where $\hat m_a$ is the conditional mean embedding fitted on arm $a$ and $\tilde w_{a,i}$ are stabilised inverse-probability weights. The statistic is $\|\hat\mu_1 - \hat\mu_0\|^2$ in the RKHS. Setting outcome_model = "zero" sets $\hat m_a \equiv 0$ and recovers the inverse-probability-weighted statistic.

Double robustness: the test is consistent if either the propensity model or the outcome (CME) model is correctly specified. Cross-fitting (cross_fit = TRUE) makes this hold under flexible machine-learning nuisances by removing own-observation overfitting bias (Chernozhukov et al., 2018).

Permutation null: the reference distribution permutes treatment labels within propensity-score bins, holding the fitted nuisances fixed. This is valid under within-bin exchangeability of treatment given the (binned) propensity score; calibration degrades as the bins coarsen relative to the propensity variation inside them.

Key advantage: unlike DML or TMLE which test only for mean shifts, DR-DATE detects any distributional difference including changes in variance, skewness, or shape.

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.

Chernozhukov, V., Chetverikov, D., Demirer, M., Duflo, E., Hansen, C., Newey, W., & Robins, J. (2018). Double/debiased machine learning for treatment and structural parameters. The Econometrics Journal, 21(1), C1-C68.

Examples

set.seed(42)
n <- 300
x <- matrix(rnorm(n * 2), n, 2)
logit_p <- 0.5 * x[, 1]
t <- rbinom(n, 1, plogis(logit_p))
y <- t * 1.0 + x[, 1] + rnorm(n, sd = 0.5)

result <- dr_date_test(y, t, x, n_permutations = 200, seed = 1)
print(result)
#> 
#>    DR-DATE Test
#> 
#> Statistic: 0.176911 
#> P-value:   0.0050 
#> N:         300 
#> Perms:     200 
#> Kernel Y:  rbf (bw = 1.249)
#> ESS:       133.7 
#>