# rdrandinf

0th

Percentile

##### Randomization Inference for RD Designs under Local Randomization

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,
wmasspoints = FALSE,
nwindows = 10,
rdwstat = "diffmeans",
approx = FALSE,
rdwreps = 1000,
level = 0.15,
plot = 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 statistic to be used in the balance tests. 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 outcome transformation model (default is 0).

evall

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

evalr

specifies the point at the right of the cutoff at which the transformed outcome is evaluated. Default is the cutoff value.

kernel

specifies the type of kernel to use as 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 name of the statistic to be used. Allowed statistics are ar (Anderson-Rubin statistic) and tsls (2SLS statistic). Default statistic is ar. The tsls statistic relies on 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 * standard deviation of outcome variable for the control group.

dscale

the fraction of the standard deviation of the outcome variable for the control group used as 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 corresponding help for details. Note: the default tlist can be narrow in some cases, which may truncate the confidence interval. We recommend the user to manually set 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 employed by the companion command rdwinselect. Default is 10.

wmin

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

wobs

the number of observations to be added at 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.

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.

rdwstat

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

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.

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

sumstats

summary statistics

obs.stat

observed statistic(s)

p.value

randomization p-value(s)

asy.pvalue

asymptotic p-value(s)

window

chosen window

ci

confidence interval (only if ci option is specified)

interf.ci

confidence interval under interferecen (only if interfci is specified)

##### References

M.D. Cattaneo, 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.

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

M.D. Cattaneo, 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.

• rdrandinf
##### Examples
# NOT RUN {
# Toy dataset
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)
# Randomization inference in window (-.75,.75), all statistics
tmp <- rdrandinf(Y,R,wl=-.75,wr=.75,statistic='all')
# 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)

# }

Documentation reproduced from package rdlocrand, version 0.7, License: GPL-2

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