Simulate Data

The code below will generate a dataset of \(n = 100\) observations. Each observation contains several observed variables:

• L1 A numeric confounder
• L2 A numeric confounder
• A A binary treatment
• Y A numeric outcome

Each observation also contains outcomes that we know only because the data are simulated. These variables are useful as ground truth in simulations.

• propensity_score The true propensity score \(P(A = 1 \mid \vec{L})\)
• Y0 The potential outcome under control
• Y1 The potential outcome under treatment

To run this code, you will need the dplyr package. If you don’t have it, first run the line install.packages("dplyr") in your R console. Then, add this line to your R script to load the package.

library(dplyr)

If you want your simulation to match our numbers exactly, add a line to set your seed.

set.seed(90095)

n <- 500
data <- tibble(
  L1 = rnorm(n),
  L2 = rnorm(n)
) |>
  # Generate potential outcomes as functions of L
  mutate(Y0 = rnorm(n(), mean = L1 + L2, sd = 1),
         Y1 = rnorm(n(), mean = Y0 + 1, sd = 1)) |>
  # Generate treatment as a function of L
  mutate(propensity_score = plogis(-2 + L1 + L2)) |>
  mutate(A = rbinom(n(), 1, propensity_score)) |>
  # Generate factual outcome
  mutate(Y = case_when(A == 0 ~ Y0,
                       A == 1 ~ Y1))

A simulation is nice because the answer is known. In this simulation, the conditional average causal effect of A on Y equals 1 at any value of L1 and L_2.