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11
Workflow·4 steps

Propensity-score weighting (PSweight)

@fan_li D · Jun 29, 2026 · 937 views
BalanceObservationalOverlap WeightsPropensity ScoreWeighting
Summary by StatsOtter

A full design-and-analysis platform for causal effects via balancing weights (overlap, IPW, ATT, matching, entropy) for binary and multiple treatments.

1

Input · what goes in

One row per unit: covariates X, a (binary or multi-level) treatment Z, and an outcome Y.

Show data format & exampleHide example
trt cov1 cov2 cov3 Y
1 0.42 1 -0.7 8.1
2 -1.1 0 0.3 5.6
1 0.05 1 1.2 9.4
3 1.30 0 -0.2 4.2
2

Pipeline · the recipe

↑ Click any step in the diagram to read its logic, code, assumptions & discussion.

1
Data prep

Load data and specify the PS model

Data preparation — shapes the raw inputs into what the estimator expects.

What happens here

Load the bundled psdata (3-level treatment trt with covariates cov1-cov6 and outcome Y) and write the propensity-score formula that all later steps reuse.

Reads from the input data Feeds into #2
Key code 
# Install:  install.packages("PSweight")
library(PSweight)
data("psdata")
head(psdata)

ps.formula  <- trt ~ cov1 + cov2 + cov3 + cov4 + cov5 + cov6
out.formula <- Y   ~ cov1 + cov2 + cov3 + cov4 + cov5 + cov6

Reference / docs ↗

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2
Diagnostic / pre-tests

Design stage: SumStat() balance check

A pre-flight check — run this before trusting any estimate downstream.

What happens here

Fit the PS model and compute weighted covariate balance under several weighting schemes before touching the outcome, so the design is finalized blind to Y.

Formula
\mathrm{ASD}_k=\frac{|\bar X_{1k}-\bar X_{0k}|}{\sqrt{(s_{1k}^2+s_{0k}^2)/2}}
Reads from #1 Feeds into #3
Key code 
bal <- SumStat(ps.formula, trtgrp = "2", data = psdata,
               weight = c("IPW", "overlap", "treated", "entropy", "matching"))

summary(bal)
plot(bal, type = "balance", metric = "ASD")

Reference / docs ↗

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3
Estimation

Estimate the ATO with overlap weights

The core estimate — where the causal quantity itself is computed.

What happens here

Call PSweight with weight='overlap' to estimate the average treatment effect among the overlap population using closed-form sandwich variance.

Formula
\hat\mu_h^{ow}=\frac{\sum_i h(x_i)\,w_{hi}\,Z_{hi}\,Y_i}{\sum_i h(x_i)\,w_{hi}\,Z_{hi}},\quad h(x)=\prod_h e_h(x)
Reads from #2 Feeds into #4
Key code 
ato1 <- PSweight(ps.formula = ps.formula, yname = "Y",
                 data = psdata, weight = "overlap")

Reference / docs ↗

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4
Inference

Summarize pairwise contrasts

Uncertainty quantification — standard errors, intervals, and aggregation.

What happens here

summary() forms the default pairwise contrasts across the three treatment levels and reports point estimates, sandwich SEs, Wald CIs, and p-values.

Formula
\hat\tau_{\mathrm{ATO}}=\frac{\sum_i w_i Z_i Y_i}{\sum_i w_i Z_i}-\frac{\sum_i w_i(1-Z_i)Y_i}{\sum_i w_i(1-Z_i)},\quad w_i=\begin{cases}1-e_i & Z_i=1\\ e_i & Z_i=0\end{cases}
Reads from #3 Feeds into the final output
Key code 
summary(ato1)

Reference / docs ↗

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3

Output · what you get

Covariate balance under IPW vs overlap weights — overlap weights drive every standardized difference to zero.
Fig 1Covariate balance under IPW vs overlap weights — overlap weights drive every standardized difference to zero.

Result figure rendered by StatsOtter from the package's documented example — unofficial community showcase; all credit to the original authors.

Result · the numbers

\hat\tau_{\mathrm{ATO}}=\frac{\sum_i w_i Z_i Y_i}{\sum_i w_i Z_i}-\frac{\sum_i w_i(1-Z_i)Y_i}{\sum_i w_i(1-Z_i)},\quad w_i=\begin{cases}1-e_i & Z_i=1\\ e_i & Z_i=0\end{cases}

⚠️ Unofficial community showcase of PSweight (docs). Not affiliated with the authors — all credit to Fan Li & coauthors; this summarizes public documentation.

What it does. PSweight estimates average causal effects from observational studies and trials using propensity-score balancing weights. It supports the overlap weight (ATO), IPW (ATE), treated weight (ATT), matching and entropy weights, for binary and multi-category treatments, with additive and ratio (risk ratio, odds ratio) estimands.

How it works. A SumStat design step fits the propensity model and reports weighted covariate balance and PS-overlap diagnostics. The PSweight analysis step computes weighted average potential outcomes and contrasts, optionally augmented (doubly robust) with an outcome model, using nuisance-adjusted sandwich (or bootstrap) standard errors. Overlap weights uniquely yield exact mean balance on covariates included in a logistic PS and minimize asymptotic variance.

Assumptions. Unconfoundedness, positivity/overlap (relaxed by ATO down-weighting extremes), correct PS model (or outcome model under augmentation), SUTVA.

What you get — Point estimate of the chosen contrast (e.g. ATO), sandwich SE, confidence interval, plus weighted balance tables and PS-overlap plots.

Example output

Closed-form inference: 

Original group value:  1, 2, 3 

Contrast: 
            1  2 3
Contrast 1 -1  1 0
Contrast 2 -1  0 1
Contrast 3  0 -1 1

           Estimate Std.Error      lwr      upr  Pr(>|z|)    
Contrast 1 -1.24161   0.16734 -1.56960 -0.91362 1.177e-13 ***
Contrast 2  1.12482   0.17099  0.78968  1.45996 4.764e-11 ***
Contrast 3  2.36643   0.25854  1.85970  2.87315 < 2.2e-16 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Links: package · paper

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