This is an example using the `star`

dataset (for more
information about the dataset, please use `?star`

).

We start with a simple example with one outcome variable (writing scores) and one machine learning algorithm (causal forest). Then we move to incoporate multiple outcomes and compare model performances with several machine learning algorithms.

To begin, we load the dataset and specify the outcome variable and
covariates to be used in the model. Next, we utilize a random forest
algorithm to develop an Individualized Treatment Rule (ITR) for
estimating the varied impacts of small class sizes on studentsâ€™ writing
scores. Since the treatment is often costly for most policy programs, we
consider a case with 20% budget constraint (`budget`

= 0.2).
The model will identify the top 20% of units who benefit from the
treatment most and assign them to with the treatment. We train the model
through sample splitting, with the `split_ratio`

between the
train and test sets determined by the `split_ratio`

argument.
Specifically, we allocate 70% of the data to train the model, while the
remaining 30% is used as testing data (`split_ratio`

=
0.7).

```
library(dplyr)
library(evalITR)
# specifying the outcome
<- "g3tlangss"
outcomes
# specifying the treatment
<- "treatment"
treatment
# specifying the data (remove other outcomes)
<- star %>% dplyr::select(-c(g3treadss,g3tmathss))
star_data
# specifying the formula
<- as.formula(
user_formula "g3tlangss ~ treatment + gender + race + birthmonth +
birthyear + SCHLURBN + GRDRANGE + GKENRMNT + GKFRLNCH +
GKBUSED + GKWHITE ")
# estimate ITR
<- estimate_itr(
fit treatment = treatment,
form = user_formula,
data = star_data,
algorithms = c("causal_forest"),
budget = 0.2,
split_ratio = 0.7)
#> Evaluate ITR under sample splitting ...
# evaluate ITR
<- evaluate_itr(fit)
est #> Cannot compute PAPDp
```

The`summary()`

function displays the following summary
statistics:

Statistics | Description |
---|---|

`PAPE` |
population average prescriptive effect |

`PAPEp` |
population average prescriptive effect with a budget constraint |

`PAPDp` |
population average prescriptive effect difference with a budget constraint (this quantity will be computed with more than 2 machine learning algorithms) |

`AUPEC` |
area under the prescriptive effect curve |

`GATE` |
grouped average treatment effects |

For more information about these evaluation metrics, please refer to Imai and Li (2021) and Imai and Li (2022).

```
# summarize estimates
summary(est)
#> -- PAPE ------------------------------------------------------------------------
#> estimate std.deviation algorithm statistic p.value
#> 1 1.2 1.3 causal_forest 0.91 0.36
#>
#> -- PAPEp -----------------------------------------------------------------------
#> estimate std.deviation algorithm statistic p.value
#> 1 1.6 1.1 causal_forest 1.4 0.15
#>
#> -- PAPDp -----------------------------------------------------------------------
#> Cannot compute PAPDp
#>
#> -- AUPEC -----------------------------------------------------------------------
#> estimate std.deviation algorithm statistic p.value
#> 1 1.3 0.96 causal_forest 1.4 0.18
#>
#> -- GATE ------------------------------------------------------------------------
#> estimate std.deviation algorithm group statistic p.value upper lower
#> 1 -210.7 107 causal_forest 1 -1.976 0.048 -386 -35
#> 2 37.4 108 causal_forest 2 0.346 0.729 -140 215
#> 3 -4.0 109 causal_forest 3 -0.037 0.971 -183 175
#> 4 7.4 108 causal_forest 4 0.068 0.945 -171 186
#> 5 195.9 108 causal_forest 5 1.813 0.070 18 374
```

We can extract estimates from the `est`

object. The
following code shows how to extract the GATE estimates for the writing
score with the causal forest algorithm. We can also plot the estimates
using the `plot_estimate()`

function and specify the type of
estimates to be plotted (`GATE`

, `PAPE`

,
`PAPEp`

, `PAPDp`

).

```
# plot GATE estimates
library(ggplot2)
<- summary(est)$GATE
gate_est
plot_estimate(gate_est, type = "GATE") +
scale_color_manual(values = c("#0072B2", "#D55E00"))
```

We plot the estimated Area Under the Prescriptive Effect Curve for the writing score across a range of budget constraints for causal forest.

```
# plot the AUPEC
plot(est)
```