**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 sample average treatment effect,
- The effect for those inclined to choose treatment,
- The effect for those disinclined to choose treatment (or, equivalent, to inclined to choose control), and
- The naive difference in the outcome between those who chose treatment rather than control.

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.

**Any scripts or data that you put into this service are public.**

Embedding an R snippet on your website

Add the following code to your website.

For more information on customizing the embed code, read Embedding Snippets.