---
title: "opl_dt_c"
output: rmarkdown::html_vignette
vignette: >
  %\VignetteIndexEntry{opl_dt_c}
  %\VignetteEngine{knitr::rmarkdown}
  %\VignetteEncoding{UTF-8}
---

```{r, include = FALSE}
knitr::opts_chunk$set(
  collapse = TRUE,
  comment = "#>"
)
```

```{r setup}
library(OPL)
```

## Introduction

The `opl_dt_c` function implements ex-ante treatment assignment using as 
                policy class a 2-layer fixed-depth decision-tree at specific
                splitting variables and threshold values.

## Usage

opl_dt_c(make_cate_result,z,w,c1=NA,c2=NA,c3=NA)

### Output

The function performs the following steps:
- Standardizes threshold variables to the [0,1] range.
- Determines optimal policy assignment using a constrained decision tree approach.
- Computes and reports key statistics, including welfare gains and percentage of treated units.
- Generates a visualization of the optimal policy assignment.

## Details

The `opl_dt_c` function follows these steps:
1. Standardizes selection variables.
2. Implements a grid search over threshold values.
3. Identifies the optimal constrained policy maximizing welfare.
4. Computes summary statistics and visualizes treatment assignment.

## Example

```r
# Example data
data_example <- data.frame(
  my_cate = runif(100, -1, 1),
  X1 = runif(100, 0, 1),
  X2 = runif(100, 0, 1),
  treatment = sample(0:1, 100, replace = TRUE)
)

# Run the decision tree-based policy learning function
opl_dt_c()
```

## Interpretation of Results

- The printed summary provides insights into constrained policy learning outcomes.
- The generated plot visualizes the treatment allocation under the optimal decision tree-based policy.

## References

- Athey, S., & Wager, S. (2021). Policy Learning with Observational Data. *Econometrica*, 89(1), 133–161.
- Cerulli, G. (2021). Improving econometric prediction by machine learning. *Applied Economics Letters*, 28(16), 1419-1425.
- Cerulli, G. (2022). Optimal treatment assignment of a learning-based constrained policy: empirical protocol and related issues. *Applied Economics Letters*. DOI: 10.1080/13504851.2022.2032577.
- Gareth, J., Witten, D., Hastie, D.T., & Tibshirani, R. (2013). *An Introduction to Statistical Learning: with Applications in R*. New York: Springer.
- Kitagawa, T., & Tetenov, A. (2018). Who Should Be Treated? Empirical Welfare Maximization Methods for Treatment Choice. *Econometrica*, 86(2), 591–616.

---

This vignette provides an overview of the `opl_dt_c` function and demonstrates its usage for decision tree-based policy learning. For further details, consult the package documentation.


## Acknowledgment
The development of this software was supported by FOSSR (Fostering Open Science in Social Science Research), a project funded by the European Union - NextGenerationEU under the NPRR Grant agreement n. MURIR0000008.
