#' Generate a sample of (X,Y) of size n
#' @param covX covariance for covariates
#' @param covY covariance for the response vector
#' @param pi   proportion for each cluster
#' @param beta regression matrix
#' @param n    sample size
#' @return list with X and Y
#' @export
#-----------------------------------------------------------------------
generateIO = function(covX, covY, pi, beta, n)
{
  size_covX = dim(covX)
  p = size_covX[1]
  k = size_covX[3]
  
  size_covY = dim(covY)
  m = size_covY[1]
  
  Y = matrix(0,n,m)
  BX = array(0, dim=c(n,m,k))
  
  require(MASS) #simulate from a multivariate normal distribution
  for (i in 1:n)
  {
    for (r in 1:k)
    {
      BXir = rep(0,m)
      for (mm in 1:m)
        Bxir[[mm]] = X[i,] %*% beta[,mm,r]
      Y[i,] = Y[i,] + pi[r] * mvrnorm(1,BXir, covY[,,r])
    }
  }
  
  return (list(X=X,Y=Y))
}