Function to generate bivariate normal data with specified correlation

correlated_data.R

## Year 2019 - 2020
## Author: Martin Papenberg

## This code is in the public domain, do with it whatever you like.
# Generate bivariate normal data with specified correlation

# param n: how many data points
# param mx: the mean of the first variable
# param my: the mean of the second variable
# param sdx: the standard deviation of the first variable
# param sdy: the standard deviation of the second variable
# param r: the observed correlation between the two measures
# param empirical: Boolean; does r refer to the correlation in the sample 
#    (-> empirical = TRUE) or the population (-> empirical = FALSE)
#
# return: the data set (two columns named `x` and `y` with random normal 
#     data generated via MASS::mvrnom)
paired_data <- function(n, mx = 0, my = 0, sdx = 1, sdy = 1, r, empirical = FALSE) {
  cor_matrix <- matrix(c(1, r, r, 1), ncol = 2)
  sds <- c(sdx, sdy)
  vars <- sds %*% t(sds)
  cov_matrix <- vars * cor_matrix
  data <- MASS::mvrnorm(
    n, 
    mu = c(mx, my), 
    Sigma = cov_matrix, 
    empirical = empirical
  ) 
  data <- data.frame(data)
  colnames(data) <- c("x", "y")
  data
}