Simulating regression models for power estimates

regression_power.r

library(tidyverse)

# Set the effect size
eff_size <- 0.2

# Function to simulate data, run regression, and check if individual predictors are significant
simulate_and_regress <- function(n) {
  data <- tibble(
    a = rnorm(n), 
    b = rnorm(n),
    c = rnorm(n),
    x = (eff_size * a) + (eff_size * b) + (eff_size * c) + rnorm(n)
  )
  
  model <- lm(x ~ a + b + c, data = data)
  p_values <- summary(model)$coefficients[, "Pr(>|t|)"]
  list(
    a_significant = p_values["a"] < 0.05,
    b_significant = p_values["b"] < 0.05,
    c_significant = p_values["c"] < 0.05
  )
}

# Function to perform simulations for a given n and return power for each predictor
simulate_power <- function(n, reps = 1000) {
  results <- replicate(reps, simulate_and_regress(n), simplify = FALSE)
  results_df <- bind_rows(results)
  power <- colMeans(results_df)
  return(power)
}

# Vector of different sample sizes
sample_sizes <- seq(from = 50, to = 250, by = 10)

# Calculate power for each sample size and each predictor
set.seed(123) # For reproducibility
power_results <- map(sample_sizes, ~ as_tibble(simulate_power(.x)))

# Combine the sample sizes and power results into a data frame
power_df <- bind_cols(tibble(sample_size = sample_sizes), bind_rows(power_results))
power_df