HOIFCar (version 1.1.1)

esti_mean_treat: Estimate treatment effect and the corresponding variance estimation on the treatment arm using different covariate adjustment methods.

Description

Implements a unified framework for comparing covariate adjustment method for completely randomized experiments under randomization-based framework.

Usage

esti_mean_treat(X, Y, A, H = NULL)

Value

A list with two named vectors:

point_est

Point estimates for all estimators:

• unadj: Unadjusted estimator

• db: Debiased estimator (Lu et al., 2023)

• adj2c: HOIF-inspired debiased estimator (Zhao et al., 2024), the same as db

• adj2: HOIF-motivated adjusted estimator (Zhao et al., 2024)

• adj3: Bias-free adjusted estimator based on adj2

• lin: Covariate-adjusted estimator (Lin, 2013)

• lin_db: Debiased estimator with population leverage scores (Lei, 2020)

var_est

Variance estimates corresponding to each estimator:

• unadj: Variance estimate for unadjusted estimator

• db: Variance estimate for debiased estimator (Lu et al., 2023)

• adj2c: Variance for adj2c, using formulas given in (Lu et al., 2023)

• adj2c_v2: Conservative variance for adj2c (Zhao et al., 2024)

• adj2: Variance for adj2, with formulas motivated by (Lu et al., 2023)

• adj2_v2: Conservative variance for adj2 (Zhao et al., 2024)

• adj3: Variance for adj3, with formulas motivated by (Lu et al., 2023)

• adj3_v2: Conservative variance for adj3 (Zhao et al., 2024)

• lin: HC3-type variance for Lin's (2013) estimator

• lin_db: HC3-type variance for Lei's (2020) estimator

Arguments

X

The n by p covariates matrix.

Y

Vector of n dimensional observed response.

A

Vector of n dimensional treatment assignment.

H

The n by n hat projection matrix corresponding to X.

References

Lin, W. (2013). Agnostic notes on regression adjustments to experimental data: Reexamining Freedman's critique. The Annals of Statistics, Vol. 7(1), 295–318, tools:::Rd_expr_doi("10.1214/12-AOAS583").
Lei, L. and Ding, P. (2020) Regression adjustment in completely randomized experiments with a diverging number of covariates. Biometrika, Vol. 108(4), 815–828, tools:::Rd_expr_doi("10.1093/biomet/asaa103").
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 <- rep(0, n)

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 <- scale(X, scale = FALSE)
H <- Xc %*% MASS::ginv(t(Xc) %*% Xc) %*% t(Xc)

result_ls <- esti_mean_treat(X, Y, A, H)
point_est <- result_ls$point_est
var_est <- result_ls$var_est
print(paste0('True mean treat:', round(mean(Y1), digits = 3), '.'))
print('Absolute bias:')
print(abs(point_est - mean(Y1)))
print('Estimate variance:')
print(var_est)