Package {AugBalWeight}

Title:	Augmented Balancing Weights as Linear Regression
Version:	0.1.0
Description:	Implements augmented balancing weights for causal inference and linear functional estimation based on David Bruns-Smith, Oliver Dukes, Avi Feller, and Elizabeth L. Ogburn (2026) <doi:10.1093/jrsssb/qkaf019>. Establishes numerical equivalence between augmented balancing weight estimators and single linear models with weighted regression coefficients. Provides flexible routines for double ridge (l2 balancing), double lasso (l-infinity balancing), and generalized augmented linear outcome models. Features cross-validation procedures for tuning outcome penalty parameters, covariate balance, and Riesz loss. Supports robust influence-function-based standard errors, bootstrap confidence intervals, balance diagnostic tools, and counterfactual prediction for treatment effects such as average treatment effect (ATE) and average treatment effect on the treated (ATT), expanding upon the doubly robust estimation framework established by Robins, Rotnitzky, and Zhao (1994) <doi:10.1080/01621459.1994.10476818> and Chernozhukov, Chetverikov, Demirer, Duflo, Hansen, Newey, and Robins (2018) <doi:10.1111/ectj.12097>.
License:	GPL (≥ 3)
Encoding:	UTF-8
LazyData:	true
Depends:	R (≥ 4.0.0)
Imports:	stats, graphics, grDevices, utils
Suggests:	testthat (≥ 3.0.0), knitr, rmarkdown
VignetteBuilder:	knitr
RoxygenNote:	7.3.3
NeedsCompilation:	no
Packaged:	2026-08-07 23:02:57 UTC; shikhar tyagi
Author:	Shikhar Tyagi [aut, cre], Arvind Pandey [aut], Bhupendra Singh [aut], Vrijesh Tripathi [aut]
Maintainer:	Shikhar Tyagi <shikhar1093tyagi@gmail.com>
Repository:	CRAN
Date/Publication:	2026-08-21 12:41:17 UTC

Average Treatment Effect (ATE) Estimation via Augmented Balancing Weights

Description

Estimates Average Treatment Effect E[Y(1) - Y(0)] using augmented balancing weights.

Usage

aug_bal_ate(
  Y,
  Z,
  X,
  type = "l2",
  outcome_model = "ridge",
  lambda = NULL,
  delta = NULL,
  tuning_method = "cv_outcome",
  alpha = 0.05
)

Arguments

Value

An object of class augbalweight representing the ATE estimator.

References

Bruns-Smith, D., Dukes, O., Feller, A., & Ogburn, E. L. (2026). Augmented balancing weights as linear regression. Journal of the Royal Statistical Society Series B: Statistical Methodology, 88(3), 699-723. doi:10.1093/jrsssb/qkaf019

Examples

set.seed(123)
n <- 120
X <- matrix(rnorm(n * 4), n, 4)
Z <- rbinom(n, 1, 0.5)
Y <- 2 * Z + X %*% c(1, -1, 0.5, 0) + rnorm(n)
fit_ate <- aug_bal_ate(Y, Z, X)
fit_ate$estimate

Average Treatment Effect on the Treated (ATT) Estimation

Description

Estimates Average Treatment Effect on the Treated E[Y(1) - Y(0) | Z = 1] using augmented balancing weights.

Usage

aug_bal_att(
  Y,
  Z,
  X,
  type = "l2",
  outcome_model = "ridge",
  lambda = NULL,
  delta = NULL,
  tuning_method = "cv_outcome",
  alpha = 0.05
)

Arguments

Value

An object of class augbalweight representing the ATT estimator.

References

Bruns-Smith, D., Dukes, O., Feller, A., & Ogburn, E. L. (2026). Augmented balancing weights as linear regression. Journal of the Royal Statistical Society Series B: Statistical Methodology, 88(3), 699-723. doi:10.1093/jrsssb/qkaf019

Examples

set.seed(123)
n <- 120
X <- matrix(rnorm(n * 4), n, 4)
Z <- rbinom(n, 1, 0.5)
Y <- 2.5 * Z + X %*% c(1, -1, 0.5, 0) + rnorm(n)
fit_att <- aug_bal_att(Y, Z, X)
fit_att$estimate

Main Fitting Function for Augmented Balancing Weights

Description

Fits augmented balancing weights for linear functional estimation and causal inference based on Bruns-Smith et al. (2026).

Usage

aug_bal_weight(
  Y,
  X_p,
  X_q,
  Z = NULL,
  estimand = c("custom", "ATE", "ATT", "ATC"),
  type = c("l2", "linf", "ols"),
  outcome_model = c("ridge", "lasso", "ols"),
  lambda = NULL,
  delta = NULL,
  tuning_method = c("cv_outcome", "cv_balance", "cv_riesz"),
  normalize = TRUE,
  nonnegative = FALSE,
  nfolds = 5,
  nboot = 0,
  alpha = 0.05
)

Arguments

Value

An object of class augbalweight containing:

References

Bruns-Smith, D., Dukes, O., Feller, A., & Ogburn, E. L. (2026). Augmented balancing weights as linear regression. Journal of the Royal Statistical Society Series B: Statistical Methodology, 88(3), 699-723. doi:10.1093/jrsssb/qkaf019

Examples

set.seed(123)
X_p <- matrix(rnorm(100 * 5), 100, 5)
Y <- X_p %*% c(1, -0.5, 2, 0, 0) + rnorm(100)
target_mean <- colMeans(matrix(rnorm(50 * 5, mean = 0.4), 50, 5))
fit <- aug_bal_weight(Y, X_p, target_mean, type = "l2", outcome_model = "ridge")
print(fit)
summary(fit)

Center Matrix Columns

Description

Centers columns of a matrix or data frame to have zero mean.

Usage

center_features(X)

Arguments

Value

A list containing centered matrix X_centered and column means means.

Extract Implied Augmented Coefficients

Description

Extract Implied Augmented Coefficients

Usage

## S3 method for class 'augbalweight'
coef(object, ...)

Arguments

Value

A numeric vector containing the implied single linear regression coefficients (beta_aug) estimated by the augmented balancing weights model.

Compute Standalone Balancing Weights

Description

Computes balancing weights w and implied feature shifts for any source and target population (Bruns-Smith et al., 2026).

Usage

compute_balancing_weights(
  X_p,
  target_mean,
  type = c("l2", "linf"),
  delta = 0.1,
  normalize = TRUE
)

Arguments

Value

A list containing:

Examples

set.seed(123)
X_p <- matrix(rnorm(60 * 3), 60, 3)
target_mean <- colMeans(matrix(rnorm(30 * 3, mean = 0.5), 30, 3))
res <- compute_balancing_weights(X_p, target_mean, type = "l2", delta = 0.1)
summary(res$weights)

Doubly Robust Influence Function Variance Computation

Description

Computes robust standard error using EIF and sandwich variance formulas.

Usage

compute_robust_se(Y, X_p, target_mean, weights, beta_aug, beta_reg)

Arguments

Value

A list with standard error se, variance var, and influence vector eif.

Lasso-Augmented L-infinity Balancing Weights (Double Lasso)

Description

Fits a lasso outcome model augmented with l-infinity balancing weights as described in Bruns-Smith et al. (2026). Demonstrates the double selection phenomenon where active features equal the union of outcome and balance sets.

Usage

double_lasso(
  Y,
  X_p,
  target_mean,
  lambda = 0.05,
  delta = 0.05,
  normalize = TRUE
)

Arguments

Value

A list containing:

References

Bruns-Smith, D., Dukes, O., Feller, A., & Ogburn, E. L. (2026). Augmented balancing weights as linear regression. Journal of the Royal Statistical Society Series B: Statistical Methodology, 88(3), 699-723. doi:10.1093/jrsssb/qkaf019

Examples

set.seed(123)
X_p <- matrix(rnorm(100 * 6), 100, 6)
Y <- X_p %*% c(2, 0, 1.5, 0, 0, -1) + rnorm(100)
target_mean <- colMeans(matrix(rnorm(50 * 6, mean = 0.3), 50, 6))
fit <- double_lasso(Y, X_p, target_mean, lambda = 0.05, delta = 0.05)
fit$estimate
fit$active_union

Ridge-Augmented L2 Balancing Weights (Double Ridge)

Description

Fits a ridge outcome model augmented with l2 balancing weights as established in Bruns-Smith et al. (2026). Computes point estimates, implied single linear regression coefficients, balancing weights, and feature shifts.

Usage

double_ridge(Y, X_p, target_mean, lambda = 0.1, delta = 0.1, normalize = TRUE)

Arguments

Value

A list containing:

References

Bruns-Smith, D., Dukes, O., Feller, A., & Ogburn, E. L. (2026). Augmented balancing weights as linear regression. Journal of the Royal Statistical Society Series B: Statistical Methodology, 88(3), 699-723. doi:10.1093/jrsssb/qkaf019

Examples

set.seed(123)
X_p <- matrix(rnorm(100 * 5), 100, 5)
Y <- X_p %*% c(1, 2, 0, -1, 0.5) + rnorm(100)
target_mean <- colMeans(matrix(rnorm(50 * 5, mean = 0.5), 50, 5))
fit <- double_ridge(Y, X_p, target_mean, lambda = 0.1, delta = 0.05)
fit$estimate

Lasso Outcome Model (Coordinate Descent)

Description

Fits a lasso regression model via coordinate descent.

Usage

fit_lasso_cd(Y, X, lambda, max_iter = 1000, tol = 1e-06)

Arguments

Value

Vector of estimated lasso coefficients.

LaLonde (1986) Job Training Demonstration Dataset

Description

A canonical dataset evaluated by LaLonde (1986) and Dehejia & Wahba (1999) from the National Supported Work (NSW) Demonstration. Used for demonstrating augmented balancing weights in causal inference and treatment effect estimation (Bruns-Smith et al., 2026).

Usage

lalonde_data

Format

A data frame with 445 observations and 12 variables:

treat

Binary treatment indicator (1 if in job training program, 0 otherwise).

age

Age of individual in years.

educ

Years of completed education.

black

Indicator for Black ethnicity (1 if Black, 0 otherwise).

hisp

Indicator for Hispanic ethnicity (1 if Hispanic, 0 otherwise).

married

Indicator for marital status (1 if married, 0 otherwise).

re74

Real earnings in 1974 (US dollars).

re75

Real earnings in 1975 (US dollars).

re78

Real earnings in 1978 (outcome variable, US dollars).

age2

Age squared.

educ2

Years of education squared.

re742

1974 earnings squared.

Source

LaLonde, R. J. (1986). Evaluating the econometric evaluations of training programs with experimental data. American Economic Review, 76(4), 604-620.

Dehejia, R. H., & Wahba, S. (1999). Causal effects in nonexperimental studies: Reevaluating the evaluation of training programs. Journal of the American Statistical Association, 94(448), 1053-1062.

Bruns-Smith, D., Dukes, O., Feller, A., & Ogburn, E. L. (2026). Augmented balancing weights as linear regression. Journal of the Royal Statistical Society Series B: Statistical Methodology, 88(3), 699-723. doi:10.1093/jrsssb/qkaf019

Diagnostic and Visualization Plot for Augmented Balancing Weights

Description

Generates balance diagnostic and covariate shift plots for an augbalweight object.

Usage

## S3 method for class 'augbalweight'
plot(x, which = 1, ...)

Arguments

Value

Invisibly returns the input augbalweight object x. Called for its side effect of generating diagnostic plots (covariate balance diagnostic when which = 1, or weight distribution histogram when which = 2).

Examples

set.seed(123)
X_p <- matrix(rnorm(80 * 4), 80, 4)
Y <- X_p %*% c(1, 2, 0, -1) + rnorm(80)
target_mean <- colMeans(matrix(rnorm(40 * 4, mean = 0.5), 40, 4))
fit <- aug_bal_weight(Y, X_p, target_mean)
plot(fit, which = 1)
plot(fit, which = 2)

Counterfactual Outcome Prediction for New Data

Description

Counterfactual Outcome Prediction for New Data

Usage

## S3 method for class 'augbalweight'
predict(object, newdata, ...)

Arguments

Value

A numeric vector of counterfactual outcome predictions for target observations in newdata, computed using the implied augmented regression coefficients.

Print Method for augbalweight

Description

Print Method for augbalweight

Usage

## S3 method for class 'augbalweight'
print(x, ...)

Arguments

Value

Invisibly returns the input augbalweight object x. Called for its side effect of printing model estimation details, point estimates, standard errors, confidence intervals, and hyperparameter settings to the console.

Print Summary for augbalweight

Description

Print Summary for augbalweight

Usage

## S3 method for class 'summary.augbalweight'
print(x, ...)

Arguments

Value

Invisibly returns the input summary.augbalweight object x. Called for its side effect of printing formatted coefficient tables and summary statistics to the console.

Safe Matrix Inversion and Ridge Solve

Description

Computes (X'X + lambda * I)^(-1) X' Y or (X'X + lambda * I)^(-1) matrix safely using SVD.

Usage

safe_ridge_inv(XtX, lambda = 0)

Arguments

Value

Inverse or regularized inverse matrix.

Soft Thresholding Operator

Description

Evaluates sign(z) * max(0, |z| - t).

Usage

soft_threshold(z, t)

Arguments

Value

Soft-thresholded numeric values.

Summary Method for augbalweight

Description

Summary Method for augbalweight

Usage

## S3 method for class 'augbalweight'
summary(object, ...)

Arguments

Value

An object of class summary.augbalweight containing structured summary statistics:

Cross-Validation Hyperparameter Tuning for Augmented Balancing Weights

Description

Automatically selects outcome penalty lambda and weighting parameter delta using CV schemes described in Bruns-Smith et al. (2026).

Usage

tune_hyperparameters(
  Y,
  X_p,
  target_mean,
  type = "l2",
  outcome_model = "ridge",
  tuning_method = "cv_outcome",
  nfolds = 5
)

Arguments

Value

A list containing optimal parameters:

Examples

set.seed(123)
X_p <- matrix(rnorm(80 * 4), 80, 4)
Y <- X_p %*% c(1, 1, -1, 0) + rnorm(80)
target_mean <- colMeans(matrix(rnorm(40 * 4, mean = 0.2), 40, 4))
tuned <- tune_hyperparameters(Y, X_p, target_mean, tuning_method = "cv_outcome")
tuned$lambda
tuned$delta

Extract Balancing Weights

Description

Extract Balancing Weights

Usage

## S3 method for class 'augbalweight'
weights(object, ...)

Arguments

Value

A numeric vector containing the estimated observation-level balancing weights for the source sample.