wt_ate: Calculate propensity score weights

In propensity: A Toolkit for Calculating and Working with Propensity Scores

Calculate propensity score weights

Description

Compute inverse probability weights for causal inference under different estimands. Each function targets a different population:

• wt_ate(): Average Treatment Effect – the full population.

• wt_att(): Average Treatment Effect on the Treated – the treated (focal) group.

• wt_atu(): Average Treatment Effect on the Untreated – the untreated (reference) group. wt_atc() is an alias.

• wt_atm(): Average Treatment Effect for the Evenly Matchable – units with the most overlap.

• wt_ato(): Average Treatment Effect for the Overlap Population – weights proportional to overlap.

• wt_entropy(): Entropy-weighted Average Treatment Effect – an entropy-balanced population.

• wt_cens(): Inverse probability of censoring weights – uses the same formula as wt_ate() but labels the estimand "uncensored". Use these to adjust for censoring in survival analysis, not for treatment weighting.

.propensity accepts a numeric vector of predicted probabilities, a data.frame of per-level probabilities, a fitted glm object, or a modified propensity score created by ps_trim(), ps_trunc(), ps_refit(), or ps_calibrate().

All functions return a psw object – a numeric vector that tracks the estimand, stabilization status, and any trimming or truncation applied.

Usage

wt_ate(
  .propensity,
  .exposure,
  .sigma = NULL,
  exposure_type = c("auto", "binary", "categorical", "continuous"),
  .focal_level = NULL,
  .reference_level = NULL,
  stabilize = FALSE,
  stabilization_score = NULL,
  ...,
  .treated = NULL,
  .untreated = NULL
)

## S3 method for class 'data.frame'
wt_ate(
  .propensity,
  .exposure,
  .sigma = NULL,
  exposure_type = c("auto", "binary", "categorical", "continuous"),
  .focal_level = NULL,
  .reference_level = NULL,
  stabilize = FALSE,
  stabilization_score = NULL,
  ...,
  .propensity_col = NULL,
  .treated = NULL,
  .untreated = NULL
)

wt_att(
  .propensity,
  .exposure,
  exposure_type = c("auto", "binary", "categorical"),
  .focal_level = NULL,
  .reference_level = NULL,
  ...,
  .treated = NULL,
  .untreated = NULL
)

## S3 method for class 'data.frame'
wt_att(
  .propensity,
  .exposure,
  exposure_type = c("auto", "binary", "categorical"),
  .focal_level = NULL,
  .reference_level = NULL,
  ...,
  .propensity_col = NULL,
  .treated = NULL,
  .untreated = NULL
)

wt_atu(
  .propensity,
  .exposure,
  exposure_type = c("auto", "binary", "categorical"),
  .focal_level = NULL,
  .reference_level = NULL,
  ...,
  .treated = NULL,
  .untreated = NULL
)

## S3 method for class 'data.frame'
wt_atu(
  .propensity,
  .exposure,
  exposure_type = c("auto", "binary", "categorical"),
  .focal_level = NULL,
  .reference_level = NULL,
  ...,
  .propensity_col = NULL,
  .treated = NULL,
  .untreated = NULL
)

wt_atm(
  .propensity,
  .exposure,
  exposure_type = c("auto", "binary", "categorical"),
  .focal_level = NULL,
  .reference_level = NULL,
  ...,
  .treated = NULL,
  .untreated = NULL
)

## S3 method for class 'data.frame'
wt_atm(
  .propensity,
  .exposure,
  exposure_type = c("auto", "binary", "categorical"),
  .focal_level = NULL,
  .reference_level = NULL,
  ...,
  .propensity_col = NULL,
  .treated = NULL,
  .untreated = NULL
)

wt_ato(
  .propensity,
  .exposure,
  exposure_type = c("auto", "binary", "categorical"),
  .focal_level = NULL,
  .reference_level = NULL,
  ...,
  .treated = NULL,
  .untreated = NULL
)

## S3 method for class 'data.frame'
wt_ato(
  .propensity,
  .exposure,
  exposure_type = c("auto", "binary", "categorical"),
  .focal_level = NULL,
  .reference_level = NULL,
  ...,
  .propensity_col = NULL,
  .treated = NULL,
  .untreated = NULL
)

wt_entropy(
  .propensity,
  .exposure,
  exposure_type = c("auto", "binary", "categorical"),
  .focal_level = NULL,
  .reference_level = NULL,
  ...,
  .treated = NULL,
  .untreated = NULL
)

## S3 method for class 'data.frame'
wt_entropy(
  .propensity,
  .exposure,
  exposure_type = c("auto", "binary", "categorical"),
  .focal_level = NULL,
  .reference_level = NULL,
  ...,
  .propensity_col = NULL,
  .treated = NULL,
  .untreated = NULL
)

wt_atc(
  .propensity,
  .exposure,
  exposure_type = c("auto", "binary", "categorical"),
  .focal_level = NULL,
  .reference_level = NULL,
  ...,
  .treated = NULL,
  .untreated = NULL
)

wt_cens(
  .propensity,
  .exposure,
  .sigma = NULL,
  exposure_type = c("auto", "binary", "categorical", "continuous"),
  .focal_level = NULL,
  .reference_level = NULL,
  stabilize = FALSE,
  stabilization_score = NULL,
  ...,
  .treated = NULL,
  .untreated = NULL
)

## S3 method for class 'data.frame'
wt_cens(
  .propensity,
  .exposure,
  .sigma = NULL,
  exposure_type = c("auto", "binary", "categorical", "continuous"),
  .focal_level = NULL,
  .reference_level = NULL,
  stabilize = FALSE,
  stabilization_score = NULL,
  ...,
  .propensity_col = NULL,
  .treated = NULL,
  .untreated = NULL
)

Arguments

.propensity	Propensity scores in one of several forms: A numeric vector of predicted probabilities (binary/continuous). A data frame or matrix with one column per exposure level (categorical), or two columns for binary (see .propensity_col). A fitted glm object – fitted values are extracted automatically. A modified propensity score created by ps_trim(), ps_trunc(), ps_refit(), or ps_calibrate().
.exposure	The exposure (treatment) variable. For binary exposures, a numeric 0/1 vector, logical, or two-level factor. For categorical exposures, a factor or character vector. For continuous exposures, a numeric vector. Optional when .propensity is a glm object (extracted from the model).
.sigma	Numeric vector of observation-level standard deviations for continuous exposures (e.g., influence(model)$sigma). Extracted automatically when .propensity is a glm object.
exposure_type	Type of exposure: "auto" (default), "binary", "categorical", or "continuous". "auto" detects the type from .exposure.
.focal_level	The value of .exposure representing the focal (treated) group. For binary exposures, defaults to the higher value. Required for wt_att() and wt_atu() with categorical exposures.
.reference_level	The value of .exposure representing the reference (control) group. Automatically detected if not supplied.
stabilize	If TRUE, multiply weights by an estimate of the marginal treatment probability (binary) or density (continuous). Only supported by wt_ate() and wt_cens(). See Stabilization in Details.
stabilization_score	Optional numeric value to use as the stabilization multiplier instead of the default (the marginal mean of .exposure). Ignored when stabilize = FALSE.
...	These dots are for future extensions and must be empty.
.treated	Use .focal_level instead.
.untreated	Use .reference_level instead.
.propensity_col	Column to use when .propensity is a data frame with a binary exposure. Accepts a column name (quoted or unquoted) or numeric index. Defaults to the second column. Ignored for categorical exposures, where all columns are used.

Details

Exposure types

All weight functions support binary exposures. wt_ate() and wt_cens() also support continuous exposures. All except wt_cens() support categorical exposures.

• Binary: .exposure is a two-level vector (e.g., 0/1, logical, or a two-level factor). .propensity is a numeric vector of P(treatment | X).

• Categorical: .exposure is a factor or character vector with 3+ levels. .propensity must be a matrix or data frame with one column per level, where rows sum to 1.

• Continuous: .exposure is a numeric vector. .propensity is a vector of conditional means (fitted values). Weights use a normal density ratio; stabilization is strongly recommended.

• Auto (default): Detects the exposure type from .exposure.

Stabilization

Setting stabilize = TRUE multiplies the base weight by an estimate of P(A) (binary) or f_A(A) (continuous), reducing variance. When no stabilization_score is supplied, the marginal mean of .exposure is used. Stabilization is supported for ATE and censoring weights (wt_ate() and wt_cens()) and is strongly recommended for continuous exposures.

Handling extreme weights

Extreme weights signal positivity violations, poor model fit, or limited overlap. You can address them by:

• Choosing an overlap-focused estimand (wt_ato(), wt_atm(), wt_entropy()), which down-weight units in regions of poor overlap.

• Trimming (ps_trim()) or truncating (ps_trunc()) propensity scores before computing weights.

• Calibrating weights with ps_calibrate().

• Stabilizing ATE weights (stabilize = TRUE).

See the halfmoon package for weight diagnostics and visualization.

Weight formulas

Binary exposures

For binary treatments (A \in \{0, 1\}), with propensity score e(X) = P(A=1 \mid X):

• ATE: w = \frac{A}{e(X)} + \frac{1-A}{1-e(X)}

• ATT: w = A + \frac{(1-A) \cdot e(X)}{1-e(X)}

• ATU: w = \frac{A \cdot (1-e(X))}{e(X)} + (1-A)

• ATM: w = \frac{\min(e(X), 1-e(X))}{A \cdot e(X) + (1-A) \cdot (1-e(X))}

• ATO: w = A \cdot (1-e(X)) + (1-A) \cdot e(X)

• Entropy: w = \frac{h(e(X))}{A \cdot e(X) + (1-A) \cdot (1-e(X))}, where h(e) = -[e \log(e) + (1-e) \log(1-e)]

Continuous exposures

Weights use the density ratio w = f_A(A) / f_{A|X}(A \mid X), where f_A is the marginal density and f_{A|X} is the conditional density (both assumed normal). Only wt_ate() and wt_cens() support continuous exposures.

Categorical exposures

For K-level treatments, weights take the tilting-function form w_i = h(\mathbf{e}_i) / e_{i,Z_i}, where e_{i,Z_i} is the propensity for unit i's observed level and h(\cdot) depends on the estimand:

• ATE: h(\mathbf{e}) = 1

• ATT: h(\mathbf{e}) = e_{\text{focal}}

• ATU: h(\mathbf{e}) = 1 - e_{\text{focal}}

• ATM: h(\mathbf{e}) = \min(e_1, \ldots, e_K)

• ATO: h(\mathbf{e}) = \bigl(\sum_k 1/e_k\bigr)^{-1}

• Entropy: h(\mathbf{e}) = -\sum_k e_k \log(e_k)

Value

A psw vector (a double vector with class psw) carrying these attributes:

• estimand: character, e.g. "ate", "att", "uncensored".

• stabilized: logical, whether stabilization was applied.

• trimmed: logical, whether the propensity scores were trimmed.

• truncated: logical, whether the propensity scores were truncated.

• calibrated: logical, whether the propensity scores were calibrated.

References

Barrett, M., D'Agostino McGowan, L., & Gerke, T. Causal Inference in R. https://www.r-causal.org/

Rosenbaum, P. R., & Rubin, D. B. (1983). The central role of the propensity score in observational studies for causal effects. Biometrika, 70(1), 41–55.

Li, L., & Greene, T. (2013). A weighting analogue to pair matching in propensity score analysis. The International Journal of Biostatistics, 9(2), 215–234. (ATM weights)

Li, F., Morgan, K. L., & Zaslavsky, A. M. (2018). Balancing covariates via propensity score weighting. Journal of the American Statistical Association, 113(521), 390–400. (ATO weights)

Zhou, Y., Matsouaka, R. A., & Thomas, L. (2020). Propensity score weighting under limited overlap and model misspecification. Statistical Methods in Medical Research, 29(12), 3721–3756. (Entropy weights)

Hirano, K., & Imbens, G. W. (2004). The propensity score with continuous treatments. In Applied Bayesian Modeling and Causal Inference from Incomplete-Data Perspectives (pp. 73–84).

Austin, P. C., & Stuart, E. A. (2015). Moving towards best practice when using inverse probability of treatment weighting (IPTW). Statistics in Medicine, 34(28), 3661–3679.

See Also

• psw() for the returned weight vector class.

• ps_trim(), ps_trunc(), ps_refit(), and ps_calibrate() for modifying propensity scores before weighting.

• ipw() for inverse-probability-weighted estimation of causal effects.

Examples

# -- Binary exposure, numeric propensity scores ----------------------
set.seed(123)
ps <- runif(100, 0.1, 0.9)
trt <- rbinom(100, 1, ps)

wt_ate(ps, trt)
wt_att(ps, trt)
wt_atu(ps, trt)
wt_atm(ps, trt)
wt_ato(ps, trt)
wt_entropy(ps, trt)

# Stabilized ATE weights (reduces variance)
wt_ate(ps, trt, stabilize = TRUE)

# Inspect the result
w <- wt_ate(ps, trt)
estimand(w)
summary(w)

# -- Overlap-focused estimands handle extreme PS better --------------
ps_extreme <- c(0.01, 0.02, 0.98, 0.99, rep(0.5, 4))
trt_extreme <- c(0, 0, 1, 1, 0, 1, 0, 1)

max(wt_ate(ps_extreme, trt_extreme))
max(wt_ato(ps_extreme, trt_extreme))

# -- From a fitted GLM -----------------------------------------------
x1 <- rnorm(100)
x2 <- rnorm(100)
trt2 <- rbinom(100, 1, plogis(0.5 * x1 + 0.3 * x2))
ps_model <- glm(trt2 ~ x1 + x2, family = binomial)

# Exposure is extracted from the model automatically
wt_ate(ps_model)

# -- Data frame input ------------------------------------------------
ps_df <- data.frame(
  control = c(0.9, 0.7, 0.3, 0.1),
  treated = c(0.1, 0.3, 0.7, 0.9)
)
exposure <- c(0, 0, 1, 1)
wt_ate(ps_df, exposure)
wt_ate(ps_df, exposure, .propensity_col = "treated")

# -- Censoring weights -----------------------------------------------
cens_ps <- runif(50, 0.6, 0.95)
cens_ind <- rbinom(50, 1, cens_ps)
wt_cens(cens_ps, cens_ind)
estimand(wt_cens(cens_ps, cens_ind))  # "uncensored"

propensity documentation built on March 3, 2026, 1:06 a.m.