R/nonnormaldata.sim.R

In tpepler/cpc: Common principal component (CPC) analysis and applications

nonnormaldata.sim <- function(Sigma, n = 100, df = rep(2, times = ncol(Sigma))){
  # Generates multivariate nonnormal data with the specified covariance structures (in Sigma)
  
  # Sigma: covariance structure for which to simulate the data
  # n: sample size
  # df: vector of chi square degrees of freedom - to control skewness of the variables (skew = sqrt(8/df))
  
  p <- ncol(Sigma)[1]
  
  xdata <- matrix(NA, nrow = n, ncol = p)
  zdata <- matrix(NA, nrow = n, ncol = p)
  for(j in 1:p){
    xdata[, j] <- rchisq(n = n, df = df[j])
    zdata[, j] <- xdata[, j] / sqrt(2 * df[j])
  }
  
  wdata <- matrix(NA, nrow = n, ncol = p)
  Sigma.eigen <- eigen(Sigma)
  sqrt.Sigma <- Sigma.eigen$vectors %*% diag(Sigma.eigen$values^0.5) %*% solve(Sigma.eigen$vectors)
  wdata <- zdata %*% sqrt.Sigma
  
  return(wdata)
}