make_cate

In OPL: Optimal Policy Learning

knitr::opts_chunk$set(
  collapse = TRUE,
  comment = "#>"
)

library(OPL)

make_cate

Predicting conditional average treatment effect (CATE) on a new policy based on the training over an old policy

Description

make_cate is a function generating conditional average treatment effect (CATE) for both a training dataset and a testing (or new) dataset related to a binary (treated vs. untreated) policy program. It provides the main input for running opl_tb (optimal policy learning of a threshold-based policy), opl_tb_c (optimal policy learning of a threshold-based policy at specific thresholds), opl_lc (optimal policy learning of a linear-combination policy), opl_lc_c (optimal policy learning of a linear-combination policy at specific parameters), opl_dt (optimal policy learning of a decision-tree policy), opl_dt_c (optimal policy learning of a decision-tree policy at specific thresholds and selection variables). Based on Kitagawa and Tetenov (2018), the main econometrics supported by these commands can be found in Cerulli (2022).

Function Syntax

make_cate(model, train_data, test_data, w, x, y, family = gaussian(), ntree = 100, mtry = 2)

Arguments:

• model: A string indicating the model to use. Valid options are "glm" and "rf".
• train_data: The training dataset used for estimating the treatment effect on the old policy.
• test_data: The test dataset used for estimating the treatment effect on the new policy.
• w: The treatment variable.
• x: Independent variables for the model.
• y: The outcome variable.
• family: The family type for the model (e.g., "binomial", "gaussian").
• ntree: Number of trees for the Random Forest model (default is 100).

Return Value

An object containing the estimated causal treatment effect results, including: - Average Treatment Effect (ATE) - Average Treatment Effect on Treated (ATET) - Average Treatment Effect on Non-Treated (ATENT)

Example Usage

set.seed(42)
train_data <- data.frame(
  y = rnorm(100),    # Outcome
  x1 = rnorm(100),   # Covariate
  x2 = rnorm(100),
  w = sample(0:1, 100, replace = TRUE)  # Trattamento
)

test_data <- data.frame(
  y = rnorm(100),    # Outcome
  x1 = rnorm(100),   # Covariate
  x2 = rnorm(100),
  w = sample(0:1, 100, replace = TRUE)  # Trattamento
)

  x <- c("x1", "x2")  # le covariate
  y <- "y"            # la variabile dipendente
  w <- "w"            # la variabile di trattamento
  family <- "gaussian"  # Famiglia per glm
  ntree <- 100          # Numero di alberi per random forest
  mtry <- 2             # Numero di variabili da considerare in ogni split

result <- make_cate(model = "glm", train_data = train_data, test_data = test_data, w = w, x = x, y = y)

Detailed Steps:

• Train and Test Data: The function separates the data into treated and untreated groups for both the training and test datasets.
• Model Estimation: The function estimates the treatment effect using either a GLM or Random Forest model. It then calculates the predicted outcome for both the treated and untreated groups.
• Causal Effect Calculation: The CATE is calculated as the difference in predicted outcomes between the treated and untreated groups.
• Output: The function returns the estimated treatment effects (ATE, ATET, ATENT) and the treatment effects for both the training and test datasets.

Results

The following results are output for both the old (training) and new (test) policy:

---

- Treatment-effects estimation: OLD POLICY -

Number of obs = [n] Estimator = regression adjustment Outcome model = linear DIM = [DIM_value] ATE = [ATE_value] ATET = [ATET_value] ATENT = [ATENT_value]

---

- Treatment-effects estimation: NEW POLICY -

Number of obs = [n] Estimator = regression adjustment Outcome model = linear DIM = [DIM_value] ATE = [ATE_value] ATET = [ATET_value] ATENT = [ATENT_value]

Conclusion

The make_cate function is a powerful tool for estimating the causal treatment effect of a policy using either GLM or Random Forest models. It provides insights into the treatment effects both for the old and new policies, making it a useful method for causal inference in policy analysis.

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.

OPL documentation built on April 4, 2025, 3:09 a.m.