In a regression discontinuity design (RDD), we have a discontinuity point at a particular covariate value, for which after that point, the treatment is assigned. In other words, we have a control (before the discontinuity point) and a treatment (everything after the discontinuity point). The main goal of the RDD is to estimate the treatment effect. This is usually done through local linear regression (LLR), where the main goal is to estimate the treatment effect at the boundary (the discontinuity point). However, it has been discovered that LLR can have poor inferential properties. This motivates the non-parametric approach used in this paper [Branson et al., 2019], which employs Gaussian process regression (GPR) to find an initial prior on the mean response functions for both our control and treatment groups. After, inference is done to estimate the treatment effect. This package will show how we can use Gaussian processes on RDDs.
You can install the development version of GPRdd from GitHub with:
# install without vignette
devtools::install_github("ejgao/GPRrdd")
# install with vignette
devtools::install_github("ejgao/GPRrdd", build_vignettes = TRUE)Upon installing, please run
library(GPRrdd)in order to gain access to the three functions that are available: gp_prior, gp_posterior, and create_plot.
Now, an example of create_plot will be shown. Since gp_prior and gp_posterior have long outputs, their usage be shown; however, the output will not be displayed. More information can be found in the vignette, however.
set.seed(100)
sc = seq(0, 1, length.out = 50)
st = seq(1, 2, length.out = 50)
yc = 1 * sc + rnorm(50, 0, 0.25)
yt = 2 + 1*st + rnorm(50, 0, 0.25)
x = c(sc, st)
x = as.matrix(x)
y = c(yc, yt)Then, to use gp_prior, we can do:
gp_prior(Xc = sc, Xt = st, Yc = yc, Yt = yt, sigma_hat = 1.2, l = 0.7)Similarly, to use gp_posterior, we can do:
gp_posterior(Xc = sc, Xt = st, Yc = yc, Yt = yt, sigma_hat = 1.2, l = 0.7)Finally, we can use create_plot to return the model fit on both the control and treatment groups, the estimated treatment effects, as well as the confidence interval around the estimated treatment effects.
create_plot(X=x, Y=y, b = 1, col_num = 1, sigma_gp = 2, sigma_hat = 1.2, choice = 1, l = 0.7)
#> $post_treatment_effect
#> [1] 1.886551
#>
#> $ci
#> [1] -0.7697033 4.5428051
Branson et al.(2019). A nonparametric Bayesian methodology for regression discontinuity designs. Journal of Statistical Planning and Inference, 202, 14-30. https://doi.org/10.1016%2Fj.jspi.2019.01.003