HOIFCar (version 1.1.1)

fit.adj2.adj2c.Random: Covariate-Adjusted Treatment Effect Estimation under the Randomization-based Framework

Description

Implements the (HOIF-inspired) debiased estimators for average treatment effect (ATE) or treatment effect on the treatment/control arm with variance estimation using asymptotic-variance. Designed for randomized experiments with moderately high-dimensional covariates.

Usage

fit.adj2.adj2c.Random(Y, X, A, pi1 = NULL, target = "ATE")

Value

A list containing three named vectors, including point estimates and variance estimates:

tau_vec

Point estimates:

• adj2: Point estimation of the HOIF-inspired debiased estimator given by Zhao et al.(2024).

• adj2c: Point estimation of the debiased estimator given by Lu et al. (2023), which is also the HOIF-inspired debiased estimator given by Zhao et al.(2024).

var_vec_v1

Variance estimates for adj2 and adj2c, with formulas inspired by Lu et al. (2023).:

• adj2: Variance for adj2.

• adj2c: Variance for adj2c.

var_vec_v2

Variance estimates for adj2 and adj2c, with formulas given in Zhao et al. (2024), which is more conservative.

• adj2: Variance for adj2.

• adj2c: Variance for adj2c.

Arguments

Y

Numeric vector of length n containing observed responses.

X

Numeric matrix (n x p) of covariates. Centering is required. Intercept term can include or not.

A

Binary vector of length n indicating treatment assignment (1 = treatment, 0 = control).

pi1

Default is NULL. The assignment probability for the randomization assignment.

target

A character string specifying the target estimand. Must be one of: - `"ATE"` (default): Average Treatment Effect (difference between treatment and control arms). - `"EY1"`: Expected outcome under treatment (estimates the effect for the treated group). - `"EY0"`: Expected outcome under control (estimates the effect for the control group).

References

Lu, X., Yang, F. and Wang, Y. (2023) Debiased regression adjustment in completely randomized experiments with moderately high-dimensional covariates. arXiv preprint, arXiv:2309.02073, tools:::Rd_expr_doi("10.48550/arXiv.2309.02073").
Zhao, S., Wang, X., Liu, L. and Zhang, X. (2024) Covariate Adjustment in Randomized Experiments Motivated by Higher-Order Influence Functions. arXiv preprint, arXiv:2411.08491, tools:::Rd_expr_doi("10.48550/arXiv.2411.08491").

Examples

set.seed(100)
n <- 500
p <- n * 0.3
beta <- runif(p, -1 / sqrt(p), 1 / sqrt(p))

X <- mvtnorm::rmvt(n, sigma = diag(1, p), df = 3)
Y1 <- as.numeric(X %*% beta)
Y0 <- as.numeric(X %*% beta - 1)

pi1 <- 2/3
n1 <- ceiling(n * pi1)
ind <- sample(n, size = n1)
A <- rep(0, n)
A[ind] <- 1
Y <- Y1 * A + Y0 * (1 - A)

Xc <- cbind(1, scale(X, scale = FALSE))
result.adj2.adj2c.random.ate.ls <- fit.adj2.adj2c.Random(Y, Xc, A, target = 'ATE')
result.adj2.adj2c.random.ate.ls

result.adj2.adj2c.random.treat.ls <- fit.adj2.adj2c.Random(Y, Xc, A, target = 'EY1')
result.adj2.adj2c.random.treat.ls

result.adj2.adj2c.random.control.ls <- fit.adj2.adj2c.Random(Y, Xc, A, target = 'EY0')
result.adj2.adj2c.random.control.ls