Draw from four-dimensional normal distribution with specific correlation structure

draw.R

#' Draw from variance-covariance matrix, given correlation rho (buggy!)
#'
#' The purpose of this function is to generate draws from
#' the variance-covariance matrix, given a specific correlation structure.
#' In particular, a four-dimensional correlation structure is drawn, in which
#' the first dimension (sales) is correlated with the remaining 3 dimensions
#' (marketing mix instruments) with *rho*, and the correlations among the 3 dimensions
#' (marketing mix instruments) is zero (or about zero).
#'
#' @param rho Correlation between the first dimension, and the remaining three dimensions
#'
#' @return N x 4 matrix, with each colun representing N draws from the variance-covariance
#' matrix.

#' @export
#'
#' @examples
#' errors <- draw_errors(.3) # works
#' errors <- draw_errors(.9) # does not work

draw_errors <- function(rho) {
  # Specify correlation matrix
  R = matrix(c(1, rho, rho, rho,
               rho, 1, 0, 0,
               rho, 0, 1, 0,
               rho, 0, 0, 1), ncol = 4)
  
  # Specify standard deviations
  S <- c(sqrt(.2), sqrt(.5), sqrt(.5), sqrt(.5))
  
  # Function to convert correlation matrix to covariance matrix
  cor2cov <- function(R, S) {
    sweep(sweep(R, 1, S, "*"), 2, S, "*")
  }
  
  # Generate covariance matrix
  Sigma = cor2cov(R, S)
  
  # Generate draws from var-covar
  error = mvrnorm(n = N,
                  mu = c(0, 0, 0, 0),
                  Sigma = Sigma)
  return(error)
}