In kolesarm/ATEHonest: Honest Inference for Treatment Effects under Unconfoundedness

library("knitr")
knitr::opts_knit$set(self.contained = FALSE)
knitr::opts_chunk$set(tidy = TRUE, collapse=TRUE, comment = "#>",
                      tidy.opts=list(blank=FALSE, width.cutoff=55))
oldoptions <- options(digits=5)

The package ATEHonest implements honest confidence intervals and estimators for estimating average treatment effects under unconfoundedness from @ak17ate. Here we illustrate the use of the package using NSW data from @DeWa99.

The data is shipped with the package, as two data frames, NSW (where the treated units are from the experimental sample and control units are from PSID), and NSWexper, where both treated and control units are from the experimental sample. We'll use the experimental sample here.

First we extract the design matrix, and the treatment and outcome vectors:

library("ATEHonest")
X <- as.matrix(NSWexper[, 2:10])
d <- NSWexper$treated
y <- NSWexper$re78

Next, we compute matrix of distances between treated and control units, using the same weight matrix to compute distances as in @ak17ate:

Ahalf <- diag(c(0.15, 0.6, 2.5, 2.5, 2.5, 0.5, 0.5, 0.1, 0.1))
D0 <- distMat(X, Ahalf, method="manhattan", d)

Next, construct a distance matrix used by the nearest neighbor variance estimator to estimate the conditional variance of the outcome. We use Mahalanobis distance:

DM <- distMat(X, chol(solve(cov(X))), method="euclidean")

We are now ready to compute the root mean squared error optimal estimator:

c1 <- ATTOptEstimate(y=y, d=d, D0=D0, C=1, DM=DM, opt.criterion="RMSE")
print(c1)

Next, we compute the estimator that's optimal for constructing two-sided CIs. We re-use the solution path returned by c1:

ATTOptEstimate(path=c1$path, C=1, DM=DM, opt.criterion="FLCI")

For computing efficiency of one- and two-sided CIs at smooth functions (see Appendix A in @ak17ate), the solution path is not long enough:

ATTEffBounds(c1$path, DM=DM, C=1)

We therefore make it longer, by passing the output c1$path as an argument to ATTOptPath (at the moment, only the ATTOptEstimate can automatically compute extra steps in the solution path as needed):

op <- ATTOptPath(path=c1$path, maxsteps=290)
ATTEffBounds(op, DM=DM, C=1)

For comparison, we also consider matching estimators. First, a matching estimator with a single match:

ATTMatchEstimate(ATTMatchPath(y, d, D0, M=1, tol=1e-12), C=1, DM=DM)

Next, we optimize the number of matches. For that we first compute the matching estimator for a vector of matches M, and then optimize the number of matches using ATTMatchEstmate:

mp <- ATTMatchPath(y, d, D0, M=1:10, tol=1e-12)
ATTMatchEstimate(mp, C=1, DM=DM, opt.criterion="FLCI")
ATTMatchEstimate(mp, C=1, DM=DM, opt.criterion="RMSE")

We can see that a single match is in fact optimal for both estimation and construction of two-sided CIs.

options(oldoptions)

References

kolesarm/ATEHonest documentation built on Nov. 14, 2020, 4:50 a.m.