Reference

-- B -- balnet() balweights() balweights.balnet() balweights.cv.balnet()

-- C -- coef.balnet() coef.cv.balnet() cv.balnet()

-- P -- plot.balnet() plot.cv.balnet() predict.balnet() predict.cv.balnet() print.balnet() print.cv.balnet()

Pathwise estimation of covariate balancing propensity scores.

Description

Fits regularized logistic regression models using covariate balancing loss functions, targeting the ATE, ATT, or treated/control means.

Usage

balnet(
  X,
  W,
  target = c("ATE", "ATT", "treated", "control"),
  sample.weights = NULL,
  max.imbalance = NULL,
  nlambda = 100L,
  lambda.min.ratio = 0.01,
  lambda = NULL,
  penalty.factor = NULL,
  groups = NULL,
  alpha = 1,
  standardize = TRUE,
  tol = 1e-07,
  maxit = as.integer(1e+05),
  verbose = FALSE,
  num.threads = 1L,
  ...
)

Arguments

X	A numeric matrix or data frame with pre-treatment covariates.
W	Treatment vector (0 = control, 1 = treated).
target	The target estimand. Default is "ATE".
sample.weights	Optional sample weights. If NULL (default), each unit receives the same weight.
max.imbalance	Optional upper bound on the standardized covariate imbalance. For lasso penalization (alpha = 1), there is a one-to-one correspondence between the penalty parameter \(\lambda\) and the maximum allowable covariate imbalance. When supplied, max.imbalance is used to adjust the lambda sequence (via lambda.min.ratio) so that the generated sequence ends at the specified imbalance level.
nlambda	Number of values for lambda if generated automatically. Default is 100.
lambda.min.ratio	Ratio of smallest to largest lambda. Default is 1e-2.
lambda	Optional lambda sequence. By default, it is constructed automatically using nlambda and lambda.min.ratio (or max.imbalance, if specified).
penalty.factor	Penalty factor per feature. Default is 1 (i.e., each feature receives the same penalty).
groups	Optional list of group indices for group penalization.
alpha	Elastic net mixing parameter. Default is 1 (lasso), 0 corresponds to ridge.
standardize	Whether to standardize the input matrix. Should only be FALSE if X already has zero-mean columns with unit variance. For target = "ATT", standardization should be based on the treated group.
tol	Coordinate descent convergence tolerance. Default is 1e-7.
maxit	Maximum number of coordinate descent iterations. Default is 1e5.
verbose	Whether to display information during fitting. Default is FALSE.
num.threads	Number of threads to use. Default is 1.
...	Additional internal arguments passed to the solver.

Details

This function aims to find balancing weights \(\hat\gamma_i\), using logistic propensity scores, that balance covariate means to a target vector, i.e.,

$$\frac{1}{n} \sum_{i=1}^n \hat\gamma_i X_i = \bar X_{\mathrm{target}}.$$

With lasso regularization (alpha = 1), imbalance is controlled in the \(\ell_\infty\) sense, allowing absolute slack of at most \(\lambda\) per covariate.

For target = "ATE", two logistic models are fit, one per arm, with

$$\hat\gamma_i^{(1)} = \frac{W_i}{\hat e^{(1)}(X_i)}, \quad \hat\gamma_i^{(0)} = \frac{1 - W_i}{1 - \hat e^{(0)}(X_i)}, \quad \bar X_{\mathrm{target}} = \frac{1}{n} \sum_{i=1}^n X_i.$$

\(\hat e^{(w)}(X_i)\) is the fitted propensity score for arm \(w\). For target = "ATT", weights balance the control means:

$$\hat\gamma_i = (1 - W_i) \frac{\hat e^{(0)}(X_i)}{1 - \hat e^{(0)}(X_i)}, \quad \bar X_{\mathrm{target}} = \frac{1}{\sum W_i} \sum_{i=1}^n W_i X_i.$$

Value

A fit balnet object.

References

Sverdrup, Erik and Trevor Hastie. "balnet: Pathwise Estimation of Covariate Balancing Propensity Scores". arXiv preprint, arXiv:2602.18577, 2026.

Examples

# Simulate data with confounding.
n <- 2000
p <- 10
X <- matrix(rnorm(n * p), n, p)
W <- rbinom(n, 1, 1 / (1.5 + exp(X[, 2] + X[, 3])))
Y <- W + 2 * log(1 + exp(X[, 1] + X[, 2] + X[, 3])) + rnorm(n)

# Fit model targeting the ATE = E[Y(1)] - E[Y(0)].
# Two logistic models are fit: one for treated, one for control.
fit <- balnet(X, W, target = "ATE")

# Print path summary.
print(fit)

#> Call:  balnet(X = X, W = W, target = "ATE") 
#> 
#> Control (path: 100/100)
#>     Nonzero Avg|SMD|   Lambda
#> 1         0 0.047050 0.195447
#> 2         1 0.046026 0.186564
#> 3         1 0.045054 0.178084
#> ...
#> 98        9 0.002111 0.002145
#> 99        9 0.002022 0.002048
#> 100       9 0.001938 0.001954
#> 
#> Treated (path: 100/100)
#>     Nonzero Avg|SMD|   Lambda
#> 1         0 0.083826 0.348217
#> 2         1 0.082751 0.332390
#> 3         1 0.081745 0.317282
#> ...
#> 98        9 0.003460 0.003822
#> 99        9 0.003309 0.003648
#> 100       9 0.003165 0.003482

# Visualize the path.
plot(fit)

# Plot the standardized covariate imbalance at given lambda.
# Note: lambda = 0 selects the final lambda in the sequence. Scalar values
# are applied to both arms.
plot(fit, lambda = 0)

# Predict propensity scores at end of lambda path.
W.hat <- predict(fit, X, lambda = 0)

# Get balancing weights at end of lambda path.
ipw.weights <- balweights(fit, lambda = 0)

# Estimate ATE using balancing weights.
mean(Y * (ipw.weights$treated - ipw.weights$control))

#> [1] 0.9165253

Extract balancing weights from a balnet object.

Description

Retrieves the estimated balancing weights \(\hat{\gamma}\). Under unconfoundedness, these correspond to inverse probability weights (IPW) for standard treatment effect estimands.

Usage

balweights(object, lambda = NULL, ...)

## S3 method for class 'balnet'
balweights(object, lambda = NULL, ...)

## S3 method for class 'cv.balnet'
balweights(object, lambda = "lambda.min", ...)

Arguments

object	A balnet object.
lambda	Value(s) of the penalty parameter lambda at which weights are required. If NULL (default), the full lambda path from the fit is used. If new values are supplied, linear interpolation is performed. For dual-arm fits (target = "ATE"), lambda can be a list or two-column matrix: the first element/column corresponds to the control arm and the second to the treatment.
...	Additional arguments (currently ignored).

Value

Estimated balancing weights (for contrast fits, target = "ATE" or "ATT", returns a list with entries for each arm).

Examples

n <- 100
p <- 25
X <- matrix(rnorm(n * p), n, p)
W <- rbinom(n, 1, 1 / (1 + exp(1 - X[, 1])))

# Fit an ATT model.
fit <- balnet(X, W, target = "ATT")

# Extract balancing weights.
wts <- balweights(fit, lambda = 0)

Extract coefficients from a balnet object.

Description

Extract coefficients from a balnet object.

Usage

## S3 method for class 'balnet'
coef(object, lambda = NULL, ...)

Arguments

object	A balnet object.
lambda	Value(s) of the penalty parameter lambda at which coefficients are required. If NULL (default), the full lambda path from the fit is used. If new values are supplied, linear interpolation is performed. For dual-arm fits (target = "ATE"), lambda can be a list or two-column matrix: the first element/column corresponds to the control arm and the second to the treatment.
...	Additional arguments (currently ignored).

Value

Estimated logistic coefficients (for dual-arm fits, returns a list with entries for each arm).

Examples

n <- 100
p <- 25
X <- matrix(rnorm(n * p), n, p)
W <- rbinom(n, 1, 1 / (1 + exp(1 - X[, 1])))

# Fit an ATT model.
fit <- balnet(X, W, target = "ATT")

# Extract coefficients.
coefs <- coef(fit)

Extract coefficients from a cv.balnet object.

Description

Extract coefficients from a cv.balnet object.

Usage

## S3 method for class 'cv.balnet'
coef(object, lambda = "lambda.min", ...)

Arguments

object	A cv.balnet object.
lambda	The lambda to use. Defaults to the cross-validated lambda.
...	Additional arguments (currently ignored).

Value

Estimated logistic coefficients (for dual-arm fits, returns a list with entries for each arm).

Examples

n <- 100
p <- 25
X <- matrix(rnorm(n * p), n, p)
W <- rbinom(n, 1, 1 / (1 + exp(1 - X[, 1])))

# Fit an ATT model.
cv.fit <- cv.balnet(X, W, target = "ATT")

# Extract coefficients at cross-validated lambda.
coefs <- coef(cv.fit)

Cross-validation for balnet.

Description

Cross-validation for balnet.

Usage

cv.balnet(
  X,
  W,
  type.measure = c("balance.loss"),
  nfolds = 10,
  foldid = NULL,
  ...
)

Arguments

X	A numeric matrix or data frame with pre-treatment covariates.
W	Treatment vector (0: control, 1: treated).
type.measure	The loss to minimize for cross-validation. Default is balance loss.
nfolds	The number of folds used for cross-validation, default is 10.
foldid	An optional n-vector specifying which fold 1 to nfold a sample belongs to. If NULL, this defaults to sample(rep(seq(nfolds), length.out = nrow(X))).
...	Arguments for balnet.

Value

A fit cv.balnet object.

Examples

n <- 100
p <- 25
X <- matrix(rnorm(n * p), n, p)
W <- rbinom(n, 1, 1 / (1 + exp(1 - X[, 1])))

# Fit an ATE model.
cv.fit <- cv.balnet(X, W)

# Print CV summary.
print(cv.fit)

#> Call:  cv.balnet(X = X, W = W) 
#> 
#> Cross-validated lambda minimizing type.measure = balance.loss:
#>  Arm     Nonzero Avg|SMD| Lambda Index
#>  Control  1      0.08159  0.1905  8   
#>  Treated 15      0.09989  0.1327 31   

# Plot at cross-validated lambda.
plot(cv.fit)

# Predict at cross-validated lambda.
W.hat <- predict(cv.fit, X)

Plot diagnostics for a balnet object.

Description

Shows effective sample size (ESS) and percent bias reduction (PBR; reduction in mean absolute imbalance) along the regularization path, computed from balancing weights and normalized to percentages. The right-hand axis maps these values to the coefficient of variation (CV) of the weights. Supplying the lambda argument displays the standardized covariate imbalance \((\bar X_{\mathrm{weighted}} - \bar X_{\mathrm{target}}) / \sigma_{\mathrm{target}}\), computed using the balancing weights at the specified lambda.

Usage

## S3 method for class 'balnet'
plot(x, lambda = NULL, groups = NULL, max = NULL, ...)

Arguments

x	A balnet object.
lambda	If NULL (default) diagnostics over the lambda path is shown. Otherwise, covariate balance at provided lambda value is shown (if target = "ATE", lambda can be a 2-vector, arm 0 and arm 1.)
groups	Optional named list of contiguous covariate index ranges to aggregate into a single variable before computing covariate imbalance (e.g., list(demographics = 4:12)).
max	The number of covariates to display in covariate balance plot. Defaults to all covariates.
...	Additional arguments.

Value

Invisibly returns the information underlying the plot.

Examples

n <- 100
p <- 25
X <- matrix(rnorm(n * p), n, p)
W <- rbinom(n, 1, 1 / (1 + exp(1 - X[, 1])))

# Fit an ATT model.
fit <- balnet(X, W, target = "ATT")

# Plot the five covariates with the largest unweighted imbalance
plot(fit, lambda = 0, max = 5)

Plot diagnostics for a cv.balnet object.

Description

Plot diagnostics for a cv.balnet object.

Usage

## S3 method for class 'cv.balnet'
plot(x, lambda = "lambda.min", ...)

Arguments

x	A cv.balnet object.
lambda	The lambda to use. Defaults to the cross-validated lambda.
...	Additional arguments.

Value

Invisibly returns the information underlying the plot.

Examples

n <- 100
p <- 25
X <- matrix(rnorm(n * p), n, p)
W <- rbinom(n, 1, 1 / (1 + exp(1 - X[, 1])))

# Fit an ATT model.
cv.fit <- cv.balnet(X, W, target = "ATT")

# Plot at cross-validated lambda.
plot(cv.fit)

Predict using a balnet object.

Description

Predict using a balnet object.

Usage

## S3 method for class 'balnet'
predict(object, newdata, lambda = NULL, type = c("response"), ...)

Arguments

object	A balnet object.
newdata	A numeric matrix.
lambda	Value(s) of the penalty parameter lambda at which coefficients are required. If NULL (default), the full lambda path from the fit is used. If new values are supplied, linear interpolation is performed. For dual-arm fits (target = "ATE"), lambda can be a list or two-column matrix: the first element/column corresponds to the control arm and the second to the treatment.
type	The type of predictions. Default is "response" (propensity scores).
...	Additional arguments (currently ignored).

Value

Estimated predictions (for dual-arm fits, returns a list with entries for each arm).

Examples

n <- 100
p <- 25
X <- matrix(rnorm(n * p), n, p)
W <- rbinom(n, 1, 1 / (1 + exp(1 - X[, 1])))

# Fit an ATT model.
fit <- balnet(X, W, target = "ATT")

# Predict propensity scores.
W.hat <- predict(fit, X)

Predict using a cv.balnet object.

Description

Predict using a cv.balnet object.

Usage

## S3 method for class 'cv.balnet'
predict(object, newdata, lambda = "lambda.min", type = c("response"), ...)

Arguments

object	A cv.balnet object.
newdata	A numeric matrix.
lambda	The lambda to use. Defaults to the cross-validated lambda.
type	The type of predictions. Default is "response" (propensity scores).
...	Additional arguments (currently ignored).

Value

Estimated predictions (for dual-arm fits, returns a list with entries for each arm).

Examples

n <- 100
p <- 25
X <- matrix(rnorm(n * p), n, p)
W <- rbinom(n, 1, 1 / (1 + exp(1 - X[, 1])))

# Fit an ATT model.
cv.fit <- cv.balnet(X, W, target = "ATT")

# Predict propensity scores at cross-validated lambda.
W.hat <- predict(cv.fit, X)

Print a balnet object.

Description

Print a balnet object.

Usage

## S3 method for class 'balnet'
print(x, digits = max(3L, getOption("digits") - 3L), max = 3, ...)

Arguments

x	A balnet object.
digits	Number of digits to print.
max	Total number of rows to show from the beginning and end of the path
...	Additional print arguments.

Value

Invisibly returns the printed information.

Examples

n <- 100
p <- 25
X <- matrix(rnorm(n * p), n, p)
W <- rbinom(n, 1, 1 / (1 + exp(1 - X[, 1])))

# Fit an ATT model.
fit <- balnet(X, W, target = "ATT")

# Print path summary.
print(fit)

#> Call:  balnet(X = X, W = W, target = "ATT") 
#> 
#> Control (path: 84/100)
#>    Nonzero Avg|SMD|  Lambda
#> 1        0  0.20579 0.89878
#> 2        1  0.20315 0.85793
#> 3        1  0.20067 0.81893
#> ...
#> 82      23  0.02072 0.02076
#> 83      23  0.01911 0.01982
#> 84      21  0.01730 0.01892

Print a cv.balnet object.

Description

Print a cv.balnet object.

Usage

## S3 method for class 'cv.balnet'
print(x, digits = max(3L, getOption("digits") - 3L), ...)

Arguments

x	A cv.balnet object.
digits	Number of digits to print.
...	Additional print arguments.

Value

Invisibly returns the printed information.

Examples

n <- 100
p <- 25
X <- matrix(rnorm(n * p), n, p)
W <- rbinom(n, 1, 1 / (1 + exp(1 - X[, 1])))

# Fit an ATT model.
cv.fit <- cv.balnet(X, W, target = "ATT")

# Print CV summary.
print(cv.fit)

#> Call:  cv.balnet(X = X, W = W, target = "ATT") 
#> 
#> Cross-validated lambda minimizing type.measure = balance.loss:
#>  Arm     Nonzero Avg|SMD| Lambda Index
#>  Control 2       0.1749   0.4733 21