Interaction Power Plot

interaction_power_plot.R

library(DeclareDesign)
library(tidyverse)

set.seed(343)

design <-
  declare_population(N = N) +
  declare_potential_outcomes(
    # Difference 1: 0.6 - 0.4 = 0.2
    Y_Z_1 = draw_binary(prob = 0.4, N = N),
    Y_Z_2 = draw_binary(prob = 0.6, N = N),
    # Difference 2: 0.6 - 0.5 = 0.1
    Y_Z_3 = draw_binary(prob = 0.5, N = N),
    Y_Z_4 = draw_binary(prob = 0.6, N = N)
    # Difference-in-differences (also called the interaction effect): 0.2 - 0.1 = 0.1
  ) +
  declare_assignment(conditions = 1:4) +
  declare_reveal(Y, Z) +
  declare_step(handler = mutate,
               Z1 = as.numeric(Z %in% c(2, 4)),
               Z2 = as.numeric(Z %in% c(3, 4))) +
  declare_estimator(Y ~ Z1 + Z2 + Z1 * Z2,
                    model = lm_robust,
                    term = "Z1:Z2")

diagnosis <-
  design %>%
  redesign(N = c(500, 1000, 3000, 5000)) %>%
  diagnose_design(sims = 500, bootstrap_sims = FALSE)

diagnosis %>%
  get_diagnosands() %>%
  ggplot(aes(N, power)) +
  geom_line() +
  geom_hline(yintercept = 0.8, linetype = "dashed") +
  theme_bw() +
  ggtitle("Power for the interaction term in a 2x2 factorial experiment",
          "When the difference in the effect of factor 1 depending on the level of factor 2 is 10pp")