In easystats/circus: The Circus of Monsters

Generate Bootstrapped data

We generated one large sample (the parent population, size 1000000) of two continuous variables producing a regression coefficient of 0.5. We then iteratively extracted a subsample of size 30, computed 3 types of coefficient (regular, bootstrapped with 1000 iterations and bootstrapped with 4000 iterations) that were subtracted from the "parent" coefficient. The closer the value is from 0, and the closer it is from the "true" effect.

Convenience Functions

generate_parent_population <- function(noise = 1, n = 10000) {
  y <- rnorm(n, 0, 1)
  x <- y + rnorm(n, 0, noise)
  return(data.frame(x = x, y = y, noise = noise))
}

extract_sample <- function(data, n = 30) {
  return(data[sample(nrow(data), n), ])
}

extract_parameters <- function(model, real = 1) {
  data.frame(
    Real = real,
    Coefficient = real - parameters::model_parameters(model)$Coefficient[2],
    Bootstrapped_1000 = real - parameters::model_parameters(model, bootstrap = TRUE, n = 1000)$Coefficient[2],
    Bootstrapped_4000 = real - parameters::model_parameters(model, bootstrap = TRUE, n = 4000)$Coefficient[2]
  )
}

Parent Population

library(dplyr)
library(ggplot2)

plots(
  generate_parent_population(noise = 0.5, n = 10000) %>%
    ggplot(aes(x = x, y = y)) +
    geom_point(size = 2, alpha = 0.1, shape = 16) +
    geom_smooth(method = "lm", se = FALSE) +
    theme_classic() +
    ggtitle("Noise = 0.5"),
  generate_parent_population(noise = 1.5, n = 10000) %>%
    ggplot(aes(x = x, y = y)) +
    geom_point(size = 2, alpha = 0.1, shape = 16) +
    geom_smooth(method = "lm", se = FALSE) +
    theme_classic() +
    ggtitle("Noise = 1.5"),
  generate_parent_population(noise = 4.5, n = 10000) %>%
    ggplot(aes(x = x, y = y)) +
    geom_point(size = 2, alpha = 0.1, shape = 16) +
    geom_smooth(method = "lm", se = FALSE) +
    theme_classic() +
    ggtitle("Noise = 4.5")
)

Creating Data

parent_model <- lm(y ~ x, data = parent)
parent_coef <- insight::get_parameters(parent_model)[2, 2]

final_data <- data.frame()

for (i in 1:10000) {
  if ((i / 100) %% 1 == 0) print(i)
  cat(".")
  sample <- extract_sample(parent, n = 30)
  model <- lm(y ~ x, data = sample)
  final_data <- rbind(final_data, extract_parameters(model, real = parent_coef))
}
write.csv(final_data, "bootstrapped.csv", row.names = FALSE)