# rdsensitivity

##### Sensitivity analysis for RD designs under local randomization

`rdsensitivity`

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

##### Usage

```
rdsensitivity(
Y,
R,
cutoff = 0,
wlist,
tlist,
statistic = "diffmeans",
p = 0,
evalat = "cutoff",
kernel = "uniform",
fuzzy = NULL,
ci,
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 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.

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

- 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 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
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.- ci
returns the confidence interval corresponding to the indicated window length.

`ci`

has to be a scalar or a two-dimensional vector, where the first value needs to be one of the values in`wlist`

. The second value, if specified, indicates the value of alpha for the confidence interval. Default alpha is .05 (95% level CI).- reps
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

treatment effects grid

window grid

table with corresponding p-values for each window and treatment effect pair.

confidence interval (if `ci`

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.

##### Examples

```
# NOT RUN {
# Toy dataset
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)
# }
```

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