Type: Package
Title: Bootstrapping for Propensity Score Analysis
Version: 1.3.9
Date: 2025-10-22
Maintainer: Jason Bryer <jason@bryer.org>
Description: It is often advantageous to test a hypothesis more than once in the context of propensity score analysis (Rosenbaum, 2012) <doi:10.1093/biomet/ass032>. The functions in this package facilitate bootstrapping for propensity score analysis (PSA). By default, bootstrapping using two classification tree methods (using 'rpart' and 'ctree' functions), two matching methods (using 'Matching' and 'MatchIt' packages), and stratification with logistic regression. A framework is described for users to implement additional propensity score methods. Visualizations are emphasized for diagnosing balance; exploring the correlation relationships between bootstrap samples and methods; and to summarize results.
License: GPL-2 | GPL-3 [expanded from: GPL]
URL: https://github.com/jbryer/PSAboot
BugReports: https://github.com/jbryer/PSAboot/issues
Depends: ggplot2, graphics, PSAgraphics, R (≥ 4.1.0)
Imports: ggthemes, Matching, MatchIt, modeltools, parallel, party, psych, reshape2, rpart, stats, TriMatch, utils
Suggests: knitr, rmarkdown
VignetteBuilder: knitr
Encoding: UTF-8
LazyLoad: yes
RoxygenNote: 7.3.2
NeedsCompilation: no
Packaged: 2025-10-22 14:46:43 UTC; jasonbryer
Author: Jason Bryer ORCID iD [aut, cre]
Repository: CRAN
Date/Publication: 2025-10-22 23:30:16 UTC

Bootstrapping for Propensity Score Analysis

Description

Bootstrapping procedures for Propensity Score Analysis.

Author(s)

Maintainer: Jason Bryer jason@bryer.org (ORCID)

See Also

Useful links:

Convert the results of PSAboot summary to a data frame.

Description

Convert the results of PSAboot summary to a data frame.

Usage

## S3 method for class 'PSAbootSummary'
as.data.frame(x, row.names = NULL, optional = FALSE, ...)

Arguments

x

results of '[summary.PSAboot()]'

row.names

row names.

optional

unused.

...

unused.

Value

a data.frame.

Returns a summary of the balance for all bootstrap samples.

Description

This method provides some crude overall measures of balance.

Usage

balance(psaboot, na.rm = TRUE, pool.fun = mean)

Arguments

psaboot

results from '[PSAboot()]'.

na.rm

should NAs be removed. NAs generally occur when there is insufficient sample for a particular covariate or an unused level.

pool.fun

a function specifying how the effect sizes across all covariates should be combined. Possible values include 'mean()' (default), 'q25()', 'q75()', 'median()', 'max()', or any function that takes a vector of numeric values.

Value

a list with three elements:

unadjusted

named numeric vector with unadjusted effect size before adjustment for each covariate

complete

a matrix with adjusted effect size for each covariate (columns) for each method (rows).

pooled

a matrix with mean adjusted effect size for all covariates for each method (columns) and each bootstrap sample (rows).

balances

a list with an M x n covariates matrix for each method.

Examples


library(PSAboot)
data(pisa.psa.cols)
data(pisausa)
bm.usa <- PSAboot(Tr = as.integer(pisausa$PUBPRIV) - 1,
    Y = pisausa$Math,
    X = pisausa[,pisa.psa.cols],
    control.ratio = 5, M = 100, seed = 2112)
bm.usa.bal <- balance(bm.usa)

Returns balance for each covariate from propensity score matching.

Description

This function is function is primarily used by [PSAboot::balance()] and probably does not need to be called directly.

Usage

balance.matching(index.treated, index.control, covs)

Arguments

index.treated

a vector with the index of treated rows in covs.

index.control

a vector with the index of control rows in covs.

covs

data frame or matrix of covariates. Factors should already be recoded. See '[cv.trans.psa()]'

Value

a named vector with one element per covariate.

Stratification using classification trees for bootstrapping.

Description

Stratification using classification trees for bootstrapping.

Usage

boot.ctree(Tr, Y, X, X.trans, formu, minStrata = 5, ...)

Arguments

Tr

vector indicating treatment assignment.

Y

vector of outcome.

X

matrix or data frame of covariates.

X.trans

a data frame of 'X' with factors recoded. See '[PSAgraphics::cv.trans.psa()]'

formu

the formula to use to estimate propensity scores. Note that the dependent varaible (i.e. treatment varaible) name will be updated using the Tr vector.

minStrata

minimum number of treatment or control units within a strata to include that strata.

...

other parameters passed from '[PSAboot()]'

Value

a list with three elements:

summary

a named numeric vector (with at minimum estimate, ci.min, and ci.max but other values allowed)

balance

a named numeric vector with one element per covariate listed in X.trans representing a balance statistic (usually standardized effect size after adjustment)

details

an arbitrary object that contains the full results of the analysis

Matching package implementation for bootstrapping.

Description

Matching package implementation for bootstrapping.

Usage

boot.matching(Tr, Y, X, X.trans, formu, estimand = "ATE", ...)

Arguments

Tr

vector indicating treatment assignment.

Y

vector of outcome.

X

matrix or data frame of covariates.

X.trans

a data frame of 'X' with factors recoded. See '[PSAgraphics::cv.trans.psa()]'

formu

the formula to use to estimate propensity scores. Note that the dependent varaible (i.e. treatment varaible) name will be updated using the Tr vector.

estimand

character string for estimand, either ATE, ATT, or ATC. See '[Matching::Match()] for more details.

...

other parameters passed to '[Matching::Match()]'.

Value

a list with three elements:

summary

a named numeric vector (with at minimum estimate, ci.min, and ci.max but other values allowed)

balance

a named numeric vector with one element per covariate listed in X.trans representing a balance statistic (usually standardized effect size after adjustment)

details

an arbitrary object that contains the full results of the analysis

MatchIt package implementation for bootstrapping.

Description

MatchIt package implementation for bootstrapping.

Usage

boot.matchit(Tr, Y, X, X.trans, formu, ...)

Arguments

Tr

vector indicating treatment assignment.

Y

vector of outcome.

X

matrix or data frame of covariates.

X.trans

a data frame of 'X' with factors recoded. See '[PSAgraphics::cv.trans.psa()]'

formu

the formula to use to estimate propensity scores. Note that the dependent varaible (i.e. treatment varaible) name will be updated using the Tr vector.

...

other parameters passed from '[PSAboot()]'

Value

a list with three elements:

summary

a named numeric vector (with at minimum estimate, ci.min, and ci.max but other values allowed)

balance

a named numeric vector with one element per covariate listed in X.trans representing a balance statistic (usually standardized effect size after adjustment)

details

an arbitrary object that contains the full results of the analysis

Stratification using classification trees for bootstrapping.

Description

Stratification using classification trees for bootstrapping.

Usage

boot.rpart(Tr, Y, X, X.trans, formu, minStrata = 5, ...)

Arguments

Tr

vector indicating treatment assignment.

Y

vector of outcome.

X

matrix or data frame of covariates.

X.trans

a data frame of 'X' with factors recoded. See '[PSAgraphics::cv.trans.psa()]'

formu

the formula to use to estimate propensity scores. Note that the dependent varaible (i.e. treatment varaible) name will be updated using the Tr vector.

minStrata

minimum number of treatment or control units within a strata to include that strata.

...

other parameters passed from '[PSAboot()]'

Value

a list with three elements:

summary

a named numeric vector (with at minimum estimate, ci.min, and ci.max but other values allowed)

balance

a named numeric vector with one element per covariate listed in X.trans representing a balance statistic (usually standardized effect size after adjustment)

details

an arbitrary object that contains the full results of the analysis

Stratification implementation for bootstrapping.

Description

Stratification implementation for bootstrapping.

Usage

boot.strata(Tr, Y, X, X.trans, formu, nstrata = 5, ...)

Arguments

Tr

vector indicating treatment assignment.

Y

vector of outcome.

X

matrix or data frame of covariates.

X.trans

a data frame of 'X' with factors recoded. See '[PSAgraphics::cv.trans.psa()]'

formu

the formula to use to estimate propensity scores. Note that the dependent varaible (i.e. treatment varaible) name will be updated using the Tr vector.

nstrata

number of strata to divide the propensity scores.

...

other parameters passed from '[PSAboot()]'

Value

a list with three elements:

summary

a named numeric vector (with at minimum estimate, ci.min, and ci.max but other values allowed)

balance

a named numeric vector with one element per covariate listed in X.trans representing a balance statistic (usually standardized effect size after adjustment)

details

an arbitrary object that contains the full results of the analysis

Propensity score weighting implementation for bootstrapping.

Description

Propensity score weighting implementation for bootstrapping.

Usage

boot.weighting(Tr, Y, X, X.trans, formu, estimand = "ATE", ...)

Arguments

Tr

vector indicating treatment assignment.

Y

vector of outcome.

X

matrix or data frame of covariates.

X.trans

a data frame of 'X' with factors recoded. See '[PSAgraphics::cv.trans.psa()]'

formu

the formula to use to estimate propensity scores. Note that the dependent varaible (i.e. treatment varaible) name will be updated using the Tr vector.

estimand

which treatment effect to estimate. Values can be ATE, ATT, ATC, or ATM.

...

other parameters passed from '[PSAboot()]'

Value

a list with three elements:

summary

a named numeric vector (with at minimum estimate, ci.min, and ci.max but other values allowed)

balance

a named numeric vector with one element per covariate listed in X.trans representing a balance statistic (usually standardized effect size after adjustment)

details

an arbitrary object that contains the full results of the analysis

Boxplot of PSA bootstrap results.

Description

Boxplot of PSA bootstrap results.

Usage

## S3 method for class 'PSAboot'
boxplot(
  x,
  bootstrap.mean.color = "blue",
  bootstrap.ci.color = "green",
  bootstrap.ci.width = 0.5,
  bootstrap.ci.size = 3,
  overall.mean.color = "red",
  tufte = FALSE,
  coord.flip = TRUE,
  ...
)

Arguments

x

result of '[PSAboot()]'.

bootstrap.mean.color

the color of the point for the bootstrap mean, or NA to omit.

bootstrap.ci.color

the color of the confidence intervals of the bootstrap samples, or NA to omit.

bootstrap.ci.width

the width of the confidence interval lines at the end.

bootstrap.ci.size

the size of the confidence interval lines.

overall.mean.color

the color of the point for the overall (before bootstrapping) mean, or NA to omit.

tufte

use Tufte's boxplot style. Requires the ggthemes package.

coord.flip

Whether to flip the coordinates.

...

unused

Value

a ggplot2 expression.

Boxplot of the balance statistics for bootstrapped samples.

Description

Boxplot of the balance statistics for bootstrapped samples.

Usage

## S3 method for class 'PSAboot.balance'
boxplot(
  x,
  unadjusted.color = "red",
  pooled.color = "blue",
  point.size = 3,
  point.alpha = 0.5,
  ...
)

Arguments

x

results of '[balance()]'

unadjusted.color

the color used for the unadjusted effect size.

pooled.color

the color used for the mean bootstrap effect size.

point.size

the size of the points.

point.alpha

the transparency level for the points.

...

other parameters passed to '[facet_wrap()]'

Value

a ggplot2 expression.

Examples


library(PSAboot)
data(pisa.psa.cols)
data(pisausa)
bm.usa <- PSAboot(Tr = as.integer(pisausa$PUBPRIV) - 1,
    Y = pisausa$Math,
    X = pisausa[,pisa.psa.cols],
    control.ratio = 5, M = 100, seed = 2112)
bm.usa.bal <- balance(bm.usa)
boxplot(bm.usa.bal, nrow = 1)

Calculates propensity score weights.

Description

Calculates propensity score weights.

Usage

calculate_ps_weights(treatment, ps, estimand = "ATE")

Arguments

treatment

a logical vector for treatment status.

ps

numeric vector of propensity scores

estimand

character string indicating which estimand to be used. Possible values are ATE (average treatment effect), ATT (average treatment effect for the treated), ATC (average treatment effect for the controls), ATM (Average Treatment Effect Among the Evenly Matched), ATO (Average Treatment Effect Among the Overlap Population)

Returns a vector with the default methods used by 'PSAboot()'.

Description

The current default methods are:

Bootstrapping has become a popular resampling method for estimating sampling distributions. And propensity score analysis (PSA) has become popular for estimating causal effects in observational studies. This function implements bootstrapping specifically for PSA. Like typical bootstrapping methods, this function estimates treatment effects for M random samples. However, unlike typical bootstrap methods, this function allows for separate sample sizes for treatment and control units. That is, under certain circumstances (e.g. when the ratio of treatment-to-control units is large) bootstrapping only the control units may be desirable. Additionally, this function provides a framework to use multiple PSA methods for each bootstrap sample.

Usage

getPSAbootMethods()

PSAboot(
  Tr,
  Y,
  X,
  M = 100,
  formu = as.formula(paste0("treat ~ ", paste0(names(X), collapse = " + "))),
  control.ratio = 5,
  control.sample.size = min(control.ratio * min(table(Tr)), max(table(Tr))),
  control.replace = TRUE,
  treated.sample.size = min(table(Tr)),
  treated.replace = TRUE,
  methods = getPSAbootMethods(),
  parallel = TRUE,
  seed = NULL,
  ...
)

Arguments

Tr

numeric (0 or 1) or logical vector of treatment indicators.

Y

vector of outcome variable

X

matrix or data frame of covariates used to estimate the propensity scores.

M

number of bootstrap samples to generate.

formu

formula used for estimating propensity scores. The default is to use all covariates in X.

control.ratio

the ratio of control units to sample relative to the treatment units.

control.sample.size

the size of each bootstrap sample of control units.

control.replace

whether to use replacement when sampling from control units.

treated.sample.size

the size of each bootstrap sample of treatment units. The default uses all treatment units for each bootstrap sample.

treated.replace

whether to use replacement when sampling from treated units.

methods

a named vector of functions for each PSA method to use.

parallel

whether to run the bootstrap samples in parallel.

seed

random seed. Each iteration, i, will use a seed of seed + i.

...

other parameters passed to '[Match()]' and '[psa.strata()]'

Details

Be sure to check the 'PSAboot' vignette for more details. The *Applied Propensity Score Analysis with R* online book also has some worked examples: https://psa.bryer.org

Value

a vector of methods for use by 'PSAboot()'

a list with following elements:

overall.summary

Data frame with the results using the complete dataset (i.e. unbootstrapped results).

overall.details

Objects returned from each method for complete dataset.

pooled.summary

Data frame with results of each bootstrap sample.

pooled.details

List of objects returned from each method for each bootstrap sample.

control.sample.size

sample size used for control units.

treated.sample.size

sample size used for treated units.

control.replace

whether control units were sampled with replacement.

treated.replace

whether treated units were sampled with replacement.

Tr

vector of treatment assignment.

Y

vector out outcome.

X

matrix or data frame of covariates.

M

number of bootstrap samples.

See Also

getPSAbootMethods

Examples


library(PSAboot)
data(pisa.psa.cols)
data(pisausa)
bm.usa <- PSAboot(Tr = as.integer(pisausa$PUBPRIV) - 1,
    Y = pisausa$Math,
    X = pisausa[,pisa.psa.cols],
    control.ratio = 5, M = 100, seed = 2112)

Histogram of PSA bootstrap results

Description

Histogram of PSA bootstrap results

Usage

## S3 method for class 'PSAboot'
hist(x, ...)

Arguments

x

result of '[PSAboot()]'.

...

other parameters passed to '[ggplot2::geom_histogram()]

Value

a ggplot2 expression.

Matrix Plot of Bootstrapped Propensity Score Analysis

Description

Matrix Plot of Bootstrapped Propensity Score Analysis

Usage

matrixplot(bm)

Arguments

bm

result from '[PSAboot()]'.

Value

Nothing returned. Creates a plot using the [graphics::pairs()] function.

Character vector representing the list of covariates used for estimating propensity scores.

Description

Character vector representing the list of covariates used for estimating propensity scores.

Format

a character vector with covariate names for estimating propensity scores.

Programme of International Student Assessment (PISA) results from the Luxembourg in 2009.

Description

Student results from the 2009 Programme of International Student Assessment (PISA) as provided by the Organization for Economic Co-operation and Development (OECD). See https://www.oecd.org/pisa/ for more information including the code book.

Format

a data frame with 4,622 rows and 65 columns.

CNT

Country

SCHOOLID

SchoolID

ST01Q01

Grade

ST04Q01

Sex

ST05Q01

Attend

ST06Q01

Age

ST07Q01

Repeat

ST08Q01

At home mother

ST08Q02

At home father

ST08Q03

At home brothers

ST08Q04

At home sisters

ST08Q05

At home grandparents

ST08Q06

At home others

ST10Q01

Mother highest schooling

ST12Q01

Mother current job status

ST14Q01

Father highest schooling

ST16Q01

Father current job status

ST19Q01

Language at home

ST20Q01

Desk

ST20Q02

Own room

ST20Q03

Study place

ST20Q04

Computer

ST20Q05

Software

ST20Q06

Internet

ST20Q07

Literature

ST20Q08

Poetry

ST20Q09

Art

ST20Q10

Textbooks

ST20Q12

Dictionary

ST20Q13

Dishwasher

ST20Q14

DVD

ST21Q01

How many cellphones

ST21Q02

How many TVs

ST21Q03

How many computers

ST21Q04

How many cars

ST21Q05

How many rooms bath or shower

ST22Q01

How many books

ST23Q01

Reading enjoyment time

ST31Q01

Enrich in test language

ST31Q02

Enrich in mathematics

ST31Q03

Enrich in science

ST31Q05

Remedial in test language

ST31Q06

Remedial in mathematics

ST31Q07

Remedial in science

ST32Q01

Out of school lessons in test language

ST32Q02

Out of school lessons maths

ST32Q03

Out of school lessons in science

PUBPRIV

Public or private school

STRATIO

Student to teacher ratio in school

Details

Note that missing values have been imputed using the mice package. Details on the specific procedure are in the pisa.impute function in the pisa package.

References

Organisation for Economic Co-operation and Development (2009). Programme for International Student Assessment (PISA).

Programme of International Student Assessment (PISA) results from the United States in 2009.

Description

Student results from the 2009 Programme of International Student Assessment (PISA) as provided by the Organization for Economic Co-operation and Development (OECD). See www.oecd.org/pisa/ for more information including the code book.

Format

a data frame with 5,233 rows and 65 columns.

CNT

Country

SCHOOLID

SchoolID

ST01Q01

Grade

ST04Q01

Sex

ST05Q01

Attend

ST06Q01

Age

ST07Q01

Repeat

ST08Q01

At home mother

ST08Q02

At home father

ST08Q03

At home brothers

ST08Q04

At home sisters

ST08Q05

At home grandparents

ST08Q06

At home others

ST10Q01

Mother highest schooling

ST12Q01

Mother current job status

ST14Q01

Father highest schooling

ST16Q01

Father current job status

ST19Q01

Language at home

ST20Q01

Desk

ST20Q02

Own room

ST20Q03

Study place

ST20Q04

Computer

ST20Q05

Software

ST20Q06

Internet

ST20Q07

Literature

ST20Q08

Poetry

ST20Q09

Art

ST20Q10

Textbooks

ST20Q12

Dictionary

ST20Q13

Dishwasher

ST20Q14

DVD

ST21Q01

How many cellphones

ST21Q02

How many TVs

ST21Q03

How many computers

ST21Q04

How many cars

ST21Q05

How many rooms bath or shower

ST22Q01

How many books

ST23Q01

Reading enjoyment time

ST31Q01

Enrich in test language

ST31Q02

Enrich in mathematics

ST31Q03

Enrich in science

ST31Q05

Remedial in test language

ST31Q06

Remedial in mathematics

ST31Q07

Remedial in science

ST32Q01

Out of school lessons in test language

ST32Q02

Out of school lessons maths

ST32Q03

Out of school lessons in science

PUBPRIV

Public or private school

STRATIO

Student to teacher ratio in school

Details

Note that missing values have been imputed using the mice package. Details on the specific procedure are in the pisa.impute function in the pisa package.

References

Organisation for Economic Co-operation and Development (2009). Programme for International Student Assessment (PISA).

Plot the results of PSAboot

Description

Plot the results of PSAboot

Usage

## S3 method for class 'PSAboot'
plot(
  x,
  sort = "all",
  ci.sig.color = "red",
  plot.overall = FALSE,
  plot.bootstrap = TRUE,
  ...
)

Arguments

x

result of '[PSAboot()]'.

sort

how the sort the rows by mean difference. Options are to sort using the mean difference from matching, stratification, both individually, or no sorting.

ci.sig.color

the color used for confidence intervals that do not span zero.

plot.overall

whether to plot vertical lines for the overall (non-bootstrapped) estimate and confidence interval.

plot.bootstrap

whether to plot vertical lines for the bootstrap pooled estimate and confidence interval.

...

currently unused.

Value

a ggplot2 expression.

Plot method for balance.

Description

Plot method for balance.

Usage

## S3 method for class 'PSAboot.balance'
plot(
  x,
  unadjusted.color = "red",
  complete.color = "blue",
  pooled.color = "black",
  ...
)

Arguments

x

results from '[balance()]'

unadjusted.color

color of the vertical line representing the mean unadjusted effect size for all covariates.

complete.color

color of the vertical line representing the mean adjusted effect size for all covariates using the complete dataset.

pooled.color

color of the vertical line representing the mean adjusted effect size for all covariates across all bootstrapped samples.

...

currently unused.

Value

a ggplot2 expression.

Examples


library(PSAboot)
data(pisa.psa.cols)
data(pisausa)
bm.usa <- PSAboot(Tr = as.integer(pisausa$PUBPRIV) - 1,
    Y = pisausa$Math,
    X = pisausa[,pisa.psa.cols],
    control.ratio = 5, M = 100, seed = 2112)
bm.usa.bal <- balance(bm.usa)
plot(bm.usa.bal)

Print results of PSAboot

Description

Print results of PSAboot

Usage

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

Arguments

x

result of '[PSAboot()]'.

...

currently unused.

Value

Nothing returned. S3 generic function that calls the [PSAboot::summary()] function.

Print method for balance.

Description

This is a crude measure of overall balance. Absolute value of the standardized effect sizes are calculated for each covariate. Overall balance statistics are the mean of those effect sizes after adjustment for each method across all bootstrap samples.

Usage

## S3 method for class 'PSAboot.balance'
print(x, na.rm = TRUE, ...)

Arguments

x

results from '[balance()]'

na.rm

whether NA balance statistics should be removed before averaging them.

...

currently unused.

Value

No valued returned.

Print method for PSAboot Summary.

Description

Print method for PSAboot Summary.

Usage

## S3 method for class 'PSAbootSummary'
print(x, digits = 3, ...)

Arguments

x

result of '[summary.PSAboot()]'

digits

desired number of digits after the decimal point.

...

unused.

Value

Nothing returned.

Propensity Score Analysis using Stratification

Description

Propensity Score Analysis using Stratification

Usage

psa.strata(Y, Tr, strata, trim = 0, minStrata = 5)

Arguments

Y

response variable.

Tr

treatment variable.

strata

strata identifier.

trim

allows for a trimmed mean as outcome measure, where trim is from 0 to .5 (.5 implying median).

minStrata

minimum number of treatment or control units within a strata to include that strata.

Value

a character vector containing summary.strata, ATE, se.wtd, approx.t, df, and CI.95.

Return the 25th percentile.

Description

Return the 25th percentile.

Usage

q25(x, na.rm = FALSE, ...)

Arguments

x

numeric vector.

na.rm

logical; if true, any NA and NaN's are removed from x before the quantiles are computed

...

other parameters passed to '[PSAboot()]'.

Value

the 25th percentile.

Returns the 75th percentile.

Description

Returns the 75th percentile.

Usage

q75(x, na.rm = FALSE, ...)

Arguments

x

numeric vector.

na.rm

logical; if true, any NA and NaN's are removed from x before the quantiles are computed

...

other parameters passed to '[PSAboot()]'.

Value

the 75th percentile.

Summary of pooled results from PSAboot

Description

Summary of pooled results from PSAboot

Usage

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

Arguments

object

result of '[PSAboot()]'.

...

currently unused.

Value

a list with pooled summary statistics.

a list with the results from easch PSA method. For each method a list contains the following elements:

sig.tot.per

Percentage of boostrap samples where the confidence interval does not span zero.

boostrap.mean

Weighted mean difference across all bootstrap samples.

boostrap.ci

Overall confidence interval across all bootstrap samples.

bootstrap.weighted.mean

Overall weighted bootstrap mean.

percent.sig

Contingency table of the number of bootstrap samples that don't span zero.

complete

Results of the summary of the PSA method.