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$y)
## Effect Estimate SE t p
## 1 t 0.8000359 0.2076146 3.853467 1.570643e-04
## 2 t_s 2.5374464 0.3327255 7.626245 9.735505e-13
## 3 t_n -2.1582576 0.5848236 -3.690442 2.889546e-04
## 4 naive 2.9034906 0.3065426 9.471736 1.554308e-15
The response structure is a data.frame containing the name of each effect, the effect estimate, and bootstrapped standard error.
A small example dataset is included that contains treatment and outcome data from Gaines and Kuklinski's (2011) study. The following code replicate the main descriptive results from Table 2 of their paper:
data(ajps)
pmean <- function(x) sprintf("%0.1f", mean(x))
cbind(
# Democrats
aggregate(cbind(therm.mccain, therm.obama) ~ tr, data = ajps[ajps$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$pid == -1, ], FUN = length)[, 2]
)
## tr therm.mccain therm.obama n_dem therm.mccain therm.obama n_rep
## 1 1 27.1 80.9 53 79.2 22.4 56
## 2 2 30.6 76.7 65 81.3 28.0 54
## 3 3 27.9 77.9 47 76.0 24.8 34
## 4 4 25.6 82.0 68 81.4 24.6 63
The paper reports four main sets of experimental results, separating the experiment by outcome (feeling thermometers for Obama and McCain) and by respondents' party identification (Democrats and Republicans).
Here are effects for McCain among Democrats:
with(ajps[ajps$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 0.6412786
Here are effects for McCain among Republicans:
with(ajps[ajps$pid == -1, ], {
estimate(rand = tr %in% 1:2, tr = tr %in% c(1,3), y = therm.mccain)
})
## Effect Estimate SE t p
## 1 t -2.1177249 3.419383 -0.6193296 0.5369916
## 2 t_s -5.0217865 8.877852 -0.5656533 0.5724746
## 3 t_n -0.5504535 4.673361 -0.1177853 0.9063932
## 4 naive -5.4444444 3.845384 -1.4158389 0.1600589
Here are effects for Obama among Democrats:
with(ajps[ajps$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 0.3892172
Here 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 0.9751897
This 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.
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