# opl_dt_c

    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

    # 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.