Choosing a functional form for the relationship between the assignment and outcome variable from a regression discontinuity design is an important step in estimating the local average treatment effect. Plotting nonparametric smoothers can suggest a functional form, and nonparametric inference may be more appropriate when a curvilinear relationship defies classification. Some researchers exclusively prefer locally-weighted regression because they feel it objectively and conservatively excludes distal observations, although the choice of bandwidth can be subjective.

The following example shows a way to obtain and plot nonparametric estimates with . The approach yields an effect size estimate of about 2.1 standard deviations, which is over twice as large as the true effect (1 *σ*) and much worse than the parametric estimates (1.1 *SD*). Increasing the default span from 0.75 to 1 (not shown) improved the estimate slightly (1.3 *SD*), as did reducing it to 0.5 (1.6 *SD*). It would be interesting to conduct a simulation study to compare parametric and nonparametric effect size recovery over many random samples while systematically varying regression functions, bandwidths, and cutoff locations.

`#Simulate and plot the data as described in the first part of the previous entry.`

#Use the full sample to fit a locally-weighted regression line.

lo <- loess(y ~ x, surface="direct")

x.lo <- min(x):max(x)

pred <- predict(lo, data.frame(x=x.lo))

lines(x.lo, pred, col="red")

#Use treatment observations to fit a locally-weighted regression line.

lo.tx <- loess(y ~ x, data.frame(y, x)[which(x<0),], surface="direct")

x.lo.tx <- 0:min(x)

pred.tx <- predict(lo.tx, data.frame(x=x.lo.tx))

lines(x.lo.tx, pred.tx, col="blue")

#Use control observations to fit a locally-weighted regression line.

lo.c <- loess(y ~ x, data.frame(y, x)[which(x>=0),], surface="direct")

x.lo.c <- 0:max(x)

pred.c <- predict(lo.c, data.frame(x=x.lo.c))

lines(x.lo.c, pred.c, col="blue")

#Add legend.

legend("bottomright", bg="white", cex=.75, pt.cex=.75, c("Treatment observation", "Control observation", "Cutoff", "Population regression line ", "Piecewise local smoother", "Full local smoother"), lty=c(NA, NA, 2, 1, 1, 1), lwd=c(NA, NA, 2, 2, 1, 1), col=c("darkgrey", "darkgrey", "darkgrey", "black", "blue", "red"), pch=c(4, 1, NA, NA, NA, NA))

#Nonparametric estimate [95% confidence interval] of local average treatement effect.

yhat.tx <- predict(lo.tx, 0, se=T)

yhat.c <- predict(lo.c, 0, se=T)

yhat.tx$fit - yhat.c$fit

c((yhat.tx$fit - qt(0.975, yhat.tx$df)*yhat.tx$se.fit) - (yhat.c$fit + qt(0.975, yhat.c$df)*yhat.c$se.fit), (yhat.tx$fit + qt(0.975, yhat.tx$df)*yhat.tx$se.fit) - (yhat.c$fit - qt(0.975, yhat.c$df)*yhat.c$se.fit))

Yields 21.28786 [7.453552, 35.122162].

Hi Christopher -

This post is great thank you. I am trying to conduct a power calculation for a clustered RD design. I was unable to find an analytical solution and was thinking of using simulations to to calculate power. However, as I am making my baby steps in R, and therefore was unable to complete the task.

Have you had any experience with running power calculation for RD design using simulated data? If so, would you be willing to share or post your code?

That would be great.

Thank you

Guy

This is really great. I am a Ph D. student and working on a paper that is a loose replication of the Lee 2008 and Caughey-Sekhon 2011 election RD design. Thanks for making the chart generating process much much easier.