GK2011 is a package for providing implementations of the treatment effect estimators for hybrid (self-selection) experiments, as developed by Gaines and Kuklinski (2011).
These functions estimate local average treatment effects for unobserved population subgroups inclined and disinclined to be treated, as revealed by a three-condition (two-arm) “hybrid” experimental design. In the design, participants are randomly assigned to one of three conditions: 1) treatment (T), 2) control (C), or 3) self-selection (S) of treatment or control. The design enables the estimation of four treatment effects:
The only function is estimate(), which provides a simple
interface for estimating all effects:
library("GK2011")
# create fake data
set.seed(12345)
d <- 
data.frame(rand = c(rep(1, 200), rep(0, 100)),
           tr = c(rep(0, 100), rep(1, 100), rep(0, 37), rep(1, 63)),
           y = c(rnorm(100), rnorm(100) + 1, rnorm(37), rnorm(63) + 3))
# estimate effects
estimate(rand = d$rand, tr = d$tr, y = d$y)##   Effect   Estimate        SE         t            p
## 1      t  0.8000359 0.2076146  3.853467 1.570643e-04
## 2    t_s  2.5374464 0.3327255  7.626245 9.735505e-13
## 3    t_n -2.1582576 0.5848236 -3.690442 2.889546e-04
## 4  naive  2.9034906 0.3065426  9.471736 1.554308e-15The response structure is a data.frame containing the name of each effect, the effect estimate, and bootstrapped standard error.
A small example dataset is included that contains treatment and outcome data from Gaines and Kuklinski’s (2011) study. The following code replicate the main descriptive results from Table 2 of their paper:
data(ajps)
pmean <- function(x) sprintf("%0.1f", mean(x))
cbind(
  # Democrats
  aggregate(cbind(therm.mccain, therm.obama) ~ tr, data = ajps[ajps$pid == 1, ], FUN = pmean)[, 1:3],
  n_dem = aggregate(therm.obama ~ tr, data = ajps[ajps$pid == 1, ], FUN = length)[, 2],
  # Republicans
  aggregate(cbind(therm.mccain, therm.obama) ~ tr, data = ajps[ajps$pid == -1, ], FUN = pmean)[, 2:3],
  n_rep = aggregate(therm.obama ~ tr, data = ajps[ajps$pid == -1, ], FUN = length)[, 2]
)##   tr therm.mccain therm.obama n_dem therm.mccain therm.obama n_rep
## 1  1         27.1        80.9    53         79.2        22.4    56
## 2  2         30.6        76.7    65         81.3        28.0    54
## 3  3         27.9        77.9    47         76.0        24.8    34
## 4  4         25.6        82.0    68         81.4        24.6    63The paper reports four main sets of experimental results, separating the experiment by outcome (feeling thermometers for Obama and McCain) and by respondents’ party identification (Democrats and Republicans).
Here are effects for McCain among Democrats:
with(ajps[ajps$pid == 1, ], {
  estimate(rand = tr %in% 1:2, tr = tr %in% c(1,3), y = therm.mccain)
})##   Effect    Estimate       SE          t         p
## 1      t  -3.5175617 4.735196 -0.7428544 0.4590587
## 2    t_s -10.0114566 9.744498 -1.0273958 0.3056205
## 3    t_n   0.9708657 7.138275  0.1360084 0.8919784
## 4  naive   2.2546934 4.826405  0.4671579 0.6412786Here are effects for McCain among Republicans:
with(ajps[ajps$pid == -1, ], {
  estimate(rand = tr %in% 1:2, tr = tr %in% c(1,3), y = therm.mccain)
})##   Effect   Estimate       SE          t         p
## 1      t -2.1177249 3.419383 -0.6193296 0.5369916
## 2    t_s -5.0217865 8.877852 -0.5656533 0.5724746
## 3    t_n -0.5504535 4.673361 -0.1177853 0.9063932
## 4  naive -5.4444444 3.845384 -1.4158389 0.1600589Here are effects for Obama among Democrats:
with(ajps[ajps$pid == 1, ], {
  estimate(rand = tr %in% 1:2, tr = tr %in% c(1,3), y = therm.obama)
})##   Effect  Estimate       SE          t         p
## 1      t  4.201451 4.458794  0.9422843 0.3479887
## 2    t_s  8.762684 9.338501  0.9383394 0.3493344
## 3    t_n  1.048835 6.703290  0.1564657 0.8758550
## 4  naive -4.040989 4.675241 -0.8643381 0.3892172Here are effects for Obama among Republicans:
with(ajps[ajps$pid == -1, ], {
  estimate(rand = tr %in% 1:2, tr = tr %in% c(1,3), y = therm.obama)
})##   Effect   Estimate        SE           t         p
## 1      t -5.5522487  5.085318 -1.09181929 0.2773200
## 2    t_s -9.4531590 13.110036 -0.72106281 0.4719932
## 3    t_n -3.4469955  7.068427 -0.48766092 0.6264927
## 4  naive  0.1774043  5.689454  0.03118125 0.9751897This package is not yet on CRAN. To install the latest development version you can pull directly from GitHub:
if(!require("ghit")){
    install.packages("ghit")
}
ghit::install_github("leeper/GK2011")Brian J. Gaines and James H. Kuklinski, (2011), “Experimental Estimation of Heterogeneous Treatment Effects Related to Self-Selection,” American Journal of Political Science 55(3): 724-736, doi:10.1111/j.1540-5907.2011.00518.x.