Help for package rdlocrand

Type:

Package

Title:

Local Randomization Methods for RD Designs

Version:

2.0

URL:

https://rdpackages.github.io/, https://github.com/rdpackages/rdlocrand

BugReports:

https://github.com/rdpackages/rdlocrand/issues

Description:

Provides tools to perform randomization inference for RD designs under local randomization: rdrandinf() to perform hypothesis testing using randomization inference, rdwinselect() to select a window around the cutoff in which randomization is likely to hold, rdsensitivity() to assess the sensitivity of the results to different window lengths and null hypotheses and rdrbounds() to construct Rosenbaum bounds for sensitivity to unobserved confounders. See Cattaneo, Titiunik and Vazquez-Bare (2016) https://rdpackages.github.io/references/Cattaneo-Titiunik-VazquezBare_2016_Stata.pdf for further methodological details, and references.

Imports:

AER, sandwich

Depends:

R (≥ 3.1)

License:

GPL-3

Encoding:

UTF-8

NeedsCompilation:

Author:

Matias D. Cattaneo [aut, cre], Rocio Titiunik [aut], Gonzalo Vazquez-Bare [aut]

Maintainer:

Matias D. Cattaneo <matias.d.cattaneo@gmail.com>

Config/roxygen2/version:

8.0.0

Packaged:

2026-05-14 10:06:10 UTC; cattaneo

Repository:

CRAN

Date/Publication:

2026-05-14 15:30:02 UTC

rdlocrand: Local Randomization Methods for RD Designs

Description

The regression discontinuity (RD) design is a popular quasi-experimental design for causal inference and policy evaluation. Under the local randomization approach, RD designs can be interpreted as randomized experiments inside a window around the cutoff. The rdlocrand package provides tools to analyze RD designs under local randomization: rdrandinf to perform hypothesis testing using randomization inference, rdwinselect to select a window around the cutoff in which randomization is likely to hold, rdsensitivity to assess sensitivity to different window lengths and null hypotheses, and rdrbounds to construct Rosenbaum bounds for sensitivity to unobserved confounders. For more details, and related R, Python, and Stata packages useful for analysis of RD designs, visit https://rdpackages.github.io/.

Author(s)

Matias D. Cattaneo, Princeton University. matias.d.cattaneo@gmail.com

Rocio Titiunik, Princeton University. rocio.titiunik@gmail.com

Gonzalo Vazquez-Bare, UC Santa Barbara. gvazquezbare@gmail.com

References

Cattaneo, M.D., B. Frandsen and R. Titiunik. (2015). Randomization Inference in the Regression Discontinuity Design: An Application to Party Advantages in the U.S. Senate. Journal of Causal Inference 3(1): 1-24.

Cattaneo, M.D., R. Titiunik and G. Vazquez-Bare. (2016). Inference in Regression Discontinuity Designs under Local Randomization. Stata Journal 16(2): 331-367.

Cattaneo, M.D., R. Titiunik and G. Vazquez-Bare. (2017). Comparing Inference Approaches for RD Designs: A Reexamination of the Effect of Head Start on Child Mortality. Journal of Policy Analysis and Management 36(3): 643-681.

Rosenbaum, P. (2002). Observational Studies. Springer.

Randomization Inference for RD Designs under Local Randomization

Description

rdrandinf implements randomization inference and related methods for RD designs, using observations in a specified or data-driven selected window around the cutoff where local randomization is assumed to hold.

Usage

rdrandinf(
  Y,
  R,
  cutoff = 0,
  wl = NULL,
  wr = NULL,
  statistic = "diffmeans",
  p = 0,
  evall = NULL,
  evalr = NULL,
  kernel = "uniform",
  fuzzy = NULL,
  nulltau = 0,
  d = NULL,
  dscale = NULL,
  ci,
  interfci = NULL,
  bernoulli = NULL,
  reps = 1000,
  seed = 666,
  quietly = FALSE,
  covariates,
  obsmin = NULL,
  wmin = NULL,
  wobs = NULL,
  wstep = NULL,
  wasymmetric = FALSE,
  wmasspoints = FALSE,
  nwindows = 10,
  dropmissing = FALSE,
  rdwstat = "diffmeans",
  approx = FALSE,
  rdwreps = 1000,
  level = 0.15,
  plot = FALSE,
  firststage = FALSE,
  obsstep = NULL
)

Arguments

Y

a vector containing the values of the outcome variable.

R

a vector containing the values of the running variable.

cutoff

the RD cutoff (default is 0).

wl

the left limit of the window. The default takes the minimum of the running variable.

wr

the right limit of the window. The default takes the maximum of the running variable.

statistic

the randomization test statistic to be used. Allowed options are diffmeans (difference in means statistic), ksmirnov (Kolmogorov-Smirnov statistic), ranksum (Wilcoxon-Mann-Whitney standardized statistic), and all. Default option is diffmeans. The statistic ttest is equivalent to diffmeans and included for backward compatibility.

p

the order of the polynomial for the outcome adjustment model (default is 0).

evall

the point to the left of the cutoff at which the adjusted outcome is evaluated. Default is the cutoff value.

evalr

the point to the right of the cutoff at which the adjusted outcome is evaluated. Default is the cutoff value.

kernel

specifies the type of kernel to use as a weighting scheme. Allowed kernel types are uniform (uniform kernel), triangular (triangular kernel), and epan (Epanechnikov kernel). Default is uniform.

fuzzy

indicates that the RD design is fuzzy. fuzzy can be specified as a vector containing the values of the endogenous treatment variable, or as a list where the first element is the vector of endogenous treatment values and the second element is a string containing the statistic to be used. Allowed statistics are ar or itt (Anderson-Rubin/intention-to-treat statistic) and tsls (2SLS statistic). Default statistic is ar. The tsls statistic relies on a large-sample approximation.

nulltau

the value of the treatment effect under the null hypothesis (default is 0).

d

the effect size for asymptotic power calculation. Default is 0.5 times the standard deviation of the outcome variable for the control group.

dscale

the fraction of the standard deviation of the outcome variable for the control group used as the alternative hypothesis for asymptotic power calculation. Default is 0.5.

ci

calculates a confidence interval for the treatment effect by test inversion. ci can be specified as a scalar or a vector, where the first element indicates the value of alpha for the confidence interval (typically 0.05 or 0.01) and the remaining elements, if specified, indicate the grid of treatment effects to be evaluated. This option uses rdsensitivity to calculate the confidence interval. See the corresponding help file for details. Note: the default tlist can be narrow in some cases, which may truncate the confidence interval. We recommend manually setting a large enough tlist.

interfci

the level for Rosenbaum's confidence interval under arbitrary interference between units.

bernoulli

the probabilities of treatment for each unit when assignment mechanism is a Bernoulli trial. This option should be specified as a vector of length equal to the length of the outcome and running variables.

reps

the number of replications (default is 1000).

seed

the seed to be used for the randomization test.

quietly

suppresses the output table.

covariates

the covariates used by rdwinselect to choose the window when wl and wr are not specified. This should be a matrix of size n x k where n is the total sample size and k is the number of covariates.

obsmin

the minimum number of observations above and below the cutoff in the smallest window used by the companion command rdwinselect. Default is 10.

wmin

the smallest window to be used (if obsmin is not specified) by the companion command rdwinselect. Specifying both wmin and obsmin returns an error.

wobs

the number of observations to be added on each side of the cutoff at each step.

wstep

the increment in window length (if obsstep is not specified) by the companion command rdwinselect. Specifying both obsstep and wstep returns an error.

wasymmetric

allows for asymmetric windows around the cutoff when wobs is specified.

wmasspoints

specifies that the running variable is discrete and each masspoint should be used as a window.

nwindows

the number of windows to be used by the companion command rdwinselect. Default is 10.

dropmissing

drop rows with missing values in covariates when calculating windows.

rdwstat

the statistic to be used by the companion command rdwinselect (see the corresponding help file for options). Default option is diffmeans.

approx

forces the companion command rdwinselect to conduct the covariate balance tests using a large-sample approximation instead of finite-sample exact randomization inference methods.

rdwreps

the number of replications to be used by the companion command rdwinselect. Default is 1000.

level

the minimum accepted value of the p-value from the covariate balance tests to be used by the companion command rdwinselect. Default is .15.

plot

draws a scatter plot of the minimum p-value from the covariate balance test against window length implemented by the companion command rdwinselect.

firststage

reports the results from the first step when using tsls.

obsstep

the minimum number of observations to be added on each side of the cutoff for the sequence of fixed-increment nested windows. Default is 2. This option is deprecated and only included for backward compatibility.

Value

A list containing:

sumstats

matrix of full-sample and window-specific summary statistics.

obs.stat

observed statistic or statistics.

p.value

randomization p-value or p-values.

asy.pvalue

asymptotic p-value or p-values.

window

chosen window endpoints.

ci

confidence interval; included only when ci is specified.

interf.ci

confidence interval under interference; included only when interfci is specified.

Author(s)

Matias D. Cattaneo, Princeton University. matias.d.cattaneo@gmail.com

Rocio Titiunik, Princeton University. rocio.titiunik@gmail.com

Gonzalo Vazquez-Bare, UC Santa Barbara. gvazquezbare@gmail.com

References

Cattaneo, M.D., R. Titiunik and G. Vazquez-Bare. (2016). Inference in Regression Discontinuity Designs under Local Randomization. Stata Journal 16(2): 331-367.

Examples

# Toy dataset
set.seed(123)
X <- array(rnorm(200),dim=c(100,2))
R <- X[,1] + X[,2] + rnorm(100)
Y <- 1 + R -.5*R^2 + .3*R^3 + (R>=0) + rnorm(100)
# Randomization inference in window (-.75,.75)
tmp <- rdrandinf(Y,R,wl=-.75,wr=.75,quietly=TRUE)
# Randomization inference in window (-.75,.75), all statistics
tmp <- rdrandinf(Y,R,wl=-.75,wr=.75,statistic='all',quietly=TRUE)
# Randomization inference with window selection
# Note: low number of replications to speed up process.
# The user should increase the number of replications.
tmp <- rdrandinf(Y,R,statistic='all',covariates=X,wmin=.5,wstep=.125,
                 rdwreps=500,level=0,quietly=TRUE)

Rosenbaum bounds for RD designs under local randomization

Description

rdrbounds calculates lower and upper bounds for the randomization p-value under different degrees of departure from a local randomized experiment, as suggested by Rosenbaum (2002).

Usage

rdrbounds(
  Y,
  R,
  cutoff = 0,
  wlist,
  gamma,
  expgamma,
  bound = "both",
  statistic = "ranksum",
  p = 0,
  evalat = "cutoff",
  kernel = "uniform",
  fuzzy = NULL,
  nulltau = 0,
  prob,
  fmpval = FALSE,
  reps = 1000,
  seed = 666
)

Arguments

Y

a vector containing the values of the outcome variable.

R

a vector containing the values of the running variable.

cutoff

the RD cutoff (default is 0).

wlist

the list of window lengths to be evaluated. By default the program constructs 10 windows around the cutoff, the first one including 10 treated and control observations and adding 5 observations to each group in subsequent windows.

gamma

the list of values of gamma to be evaluated.

expgamma

the list of values of exp(gamma) to be evaluated. Default is c(1.5,2,2.5,3).

bound

specifies which bounds the command calculates. Options are upper for upper bound, lower for lower bound, and both for both upper and lower bounds. Default is both.

statistic

the randomization test statistic to be used. Allowed options are diffmeans (difference in means statistic), ksmirnov (Kolmogorov-Smirnov statistic), and ranksum (Wilcoxon-Mann-Whitney standardized statistic). Default option is ranksum. The statistic ttest is equivalent to diffmeans and included for backward compatibility.

p

the order of the polynomial for the outcome adjustment model. Default is 0.

evalat

specifies the point at which the adjusted variable is evaluated. Allowed options are cutoff and means. Default is cutoff.

kernel

fuzzy

indicates that the RD design is fuzzy. fuzzy should be specified as a vector containing the values of the endogenous treatment variable. This option uses an Anderson-Rubin/intention-to-treat statistic.

nulltau

the value of the treatment effect under the null hypothesis. Default is 0.

prob

the probabilities of treatment for each unit when the assignment mechanism is a Bernoulli trial. This option should be specified as a vector of length equal to the length of the outcome and running variables.

fmpval

reports the p-value under fixed margins randomization, in addition to the p-value under Bernoulli trials.

reps

the number of replications. Default is 1000.

seed

the seed to be used for the randomization tests.

Value

A list containing:

gamma

vector of gamma values.

expgamma

vector of exp(gamma) values.

wlist

window grid.

p.values

p-values for each window under gamma = 0. When fmpval = TRUE, this includes Bernoulli and fixed-margins p-values.

lower.bound

matrix of lower-bound p-values for each gamma-window pair; included when bound = "lower" or bound = "both".

upper.bound

matrix of upper-bound p-values for each gamma-window pair; included when bound = "upper" or bound = "both".

Author(s)

Matias D. Cattaneo, Princeton University. matias.d.cattaneo@gmail.com

Rocio Titiunik, Princeton University. rocio.titiunik@gmail.com

Gonzalo Vazquez-Bare, UC Santa Barbara. gvazquezbare@gmail.com

References

Cattaneo, M.D., R. Titiunik and G. Vazquez-Bare. (2016). Inference in Regression Discontinuity Designs under Local Randomization. Stata Journal 16(2): 331-367.

Rosenbaum, P. (2002). Observational Studies. Springer.

Examples

# Toy dataset
set.seed(123)
R <- runif(100,-1,1)
Y <- 1 + R -.5*R^2 + .3*R^3 + (R>=0) + rnorm(100)
# Rosenbaum bounds
# Note: low number of replications and windows to speed up process.
# The user should increase these values.
rdrbounds(Y,R,expgamma=c(1.5,2),wlist=c(.3),reps=100)

Sensitivity analysis for RD designs under local randomization

Description

rdsensitivity analyzes the sensitivity of randomization p-values and confidence intervals to different window lengths.

Usage

rdsensitivity(
  Y,
  R,
  cutoff = 0,
  wlist,
  wlist_left,
  tlist,
  statistic = "diffmeans",
  p = 0,
  evalat = "cutoff",
  kernel = "uniform",
  fuzzy = NULL,
  ci = NULL,
  ci_alpha = 0.05,
  reps = 1000,
  seed = 666,
  nodraw = FALSE,
  quietly = FALSE
)

Arguments

Y

a vector containing the values of the outcome variable.

R

a vector containing the values of the running variable.

cutoff

the RD cutoff (default is 0).

wlist

the list of windows to the right of the cutoff. By default the program constructs 10 windows around the cutoff with 5 observations each.

wlist_left

the list of windows to the left of the cutoff. If not specified, the windows are constructed symmetrically around the cutoff based on the values in wlist.

tlist

the list of treatment-effect values under the null to be evaluated. By default the program uses ten evenly spaced points within the asymptotic confidence interval for a constant treatment effect in the smallest window to be used.

statistic

the randomization test statistic to be used. Allowed options are diffmeans (difference in means statistic), ksmirnov (Kolmogorov-Smirnov statistic), and ranksum (Wilcoxon-Mann-Whitney standardized statistic). Default option is diffmeans. The statistic ttest is equivalent to diffmeans and included for backward compatibility.

p

the order of the polynomial for the outcome adjustment model. Default is 0.

evalat

specifies the point at which the adjusted variable is evaluated. Allowed options are cutoff and means. Default is cutoff.

kernel

fuzzy

ci

returns the confidence interval corresponding to the indicated window length. ci must be a two-element vector containing the left and right limits of the window. Default alpha is .05 (95% level CI).

ci_alpha

specifies the value of alpha for the confidence interval. Default alpha is .05 (95% level CI).

reps

the number of replications. Default is 1000.

seed

the seed to be used for the randomization tests.

nodraw

suppresses contour plot.

quietly

suppresses the output table.

Value

A list containing:

tlist

treatment-effect grid.

wlist

right endpoints of the window grid.

wlist_left

left endpoints of the window grid.

results

matrix of p-values for each treatment-effect and window pair.

ci

confidence interval; included only when ci is specified.

Author(s)

Matias D. Cattaneo, Princeton University. matias.d.cattaneo@gmail.com

Rocio Titiunik, Princeton University. rocio.titiunik@gmail.com

Gonzalo Vazquez-Bare, UC Santa Barbara. gvazquezbare@gmail.com

References

Cattaneo, M.D., R. Titiunik and G. Vazquez-Bare. (2016). Inference in Regression Discontinuity Designs under Local Randomization. Stata Journal 16(2): 331-367.

Examples

# Toy dataset
set.seed(123)
R <- runif(100,-1,1)
Y <- 1 + R -.5*R^2 + .3*R^3 + (R>=0) + rnorm(100)
# Sensitivity analysis
# Note: low number of replications to speed up process.
# The user should increase the number of replications.
tmp <- rdsensitivity(Y,R,wlist=seq(.75,2,by=.25),tlist=seq(0,5,by=1),
                     reps=500,nodraw=TRUE,quietly=TRUE)

Window selection for RD designs under local randomization

Description

rdwinselect implements a window-selection procedure based on balance tests for RD designs under local randomization. Specifically, it constructs a sequence of nested windows around the RD cutoff and reports binomial tests for the running variable and covariate balance tests for the covariates (if specified). The recommended window is the largest window around the cutoff such that the minimum p-value from the balance tests is larger than a prespecified level for all nested (smaller) windows. By default, the p-values are calculated using randomization inference methods.

Usage

rdwinselect(
  R,
  X,
  cutoff = 0,
  obsmin = NULL,
  wmin = NULL,
  wobs = NULL,
  wstep = NULL,
  wasymmetric = FALSE,
  wmasspoints = FALSE,
  dropmissing = FALSE,
  nwindows = 10,
  statistic = "diffmeans",
  p = 0,
  evalat = "cutoff",
  kernel = "uniform",
  approx = FALSE,
  level = 0.15,
  reps = 1000,
  seed = 666,
  plot = FALSE,
  quietly = FALSE,
  obsstep = NULL
)

Arguments

R

a vector containing the values of the running variable.

X

the matrix of covariates to be used in the balance tests. The matrix is optional, but the recommended window is only provided when at least one covariate is specified. This should be a matrix of size n x k where n is the total sample size and k is the number of covariates.

cutoff

the RD cutoff (default is 0).

obsmin

the minimum number of observations above and below the cutoff in the smallest window. Default is 10.

wmin

the smallest window to be used.

wobs

the number of observations to be added on each side of the cutoff at each step. Default is 5.

wstep

the increment in window length.

wasymmetric

allows for asymmetric windows around the cutoff when wobs is specified.

wmasspoints

specifies that the running variable is discrete and each masspoint should be used as a window.

dropmissing

drop rows with missing values in covariates when calculating windows.

nwindows

the number of windows to be used. Default is 10.

statistic

the statistic to be used in the balance tests. Allowed options are diffmeans (difference in means statistic), ksmirnov (Kolmogorov-Smirnov statistic), ranksum (Wilcoxon-Mann-Whitney standardized statistic) and hotelling (Hotelling's T-squared statistic). Default option is diffmeans. The statistic ttest is equivalent to diffmeans and included for backward compatibility.

p

the order of the polynomial for the outcome adjustment model (for covariates). Default is 0.

evalat

specifies the point at which the adjusted variable is evaluated. Allowed options are cutoff and means. Default is cutoff.

kernel

approx

forces the command to conduct the covariate balance tests using a large-sample approximation instead of finite-sample exact randomization inference methods.

level

the minimum accepted value of the p-value from the covariate balance tests. Default is .15.

reps

the number of replications. Default is 1000.

seed

the seed to be used for the randomization tests.

plot

draws a scatter plot of the minimum p-value from the covariate balance test against window length.

quietly

suppresses output.

obsstep

the minimum number of observations to be added on each side of the cutoff for the sequence of fixed-increment nested windows. This option is deprecated and only included for backward compatibility.

Value

A list containing:

w_left

left endpoint of the recommended window.

w_right

right endpoint of the recommended window.

wlist_left

left endpoints of the candidate windows.

wlist_right

right endpoints of the candidate windows.

results

matrix containing the minimum covariate-balance p-value, selected covariate index, binomial-test p-value, sample sizes below and above the cutoff, and window endpoints for each candidate window.

summary

matrix of sample-size summaries by side of the cutoff.

Author(s)

Matias D. Cattaneo, Princeton University. matias.d.cattaneo@gmail.com

Rocio Titiunik, Princeton University. rocio.titiunik@gmail.com

Gonzalo Vazquez-Bare, UC Santa Barbara. gvazquezbare@gmail.com

References

Cattaneo, M.D., R. Titiunik and G. Vazquez-Bare. (2016). Inference in Regression Discontinuity Designs under Local Randomization. Stata Journal 16(2): 331-367.

Examples

# Toy dataset
set.seed(123)
X <- array(rnorm(200),dim=c(100,2))
R <- X[,1] + X[,2] + rnorm(100)
# Window selection adding 5 observations at each step
# Note: low number of replications to speed up process.
tmp <- rdwinselect(R,X,obsmin=10,wobs=5,nwindows=5,reps=500,quietly=TRUE)
# Window selection setting initial window and step
# The user should increase the number of replications.
tmp <- rdwinselect(R,X,wmin=.5,wstep=.125,reps=500,quietly=TRUE)
# Window selection with approximate (large sample) inference and p-value plot
tmp <- rdwinselect(R,X,wmin=.5,wstep=.125,approx=TRUE,nwindows=20,quietly=TRUE,plot=TRUE)

Package {rdlocrand}

rdlocrand: Local Randomization Methods for RD Designs

Description

Author(s)

References

See Also

Randomization Inference for RD Designs under Local Randomization

Description

Usage

Arguments

Value

Author(s)

References

Examples

Rosenbaum bounds for RD designs under local randomization

Description

Usage

Arguments

Value

Author(s)

References

Examples

Sensitivity analysis for RD designs under local randomization

Description

Usage

Arguments

Value

Author(s)

References

Examples

Window selection for RD designs under local randomization

Description

Usage

Arguments

Value

Author(s)

References

Examples