Generating random variables with specific correlation threshold value - r

Question

I am generating random variables with specified range and dimension.I have made a following code for this.
generateRandom <- function(size,scale){
result<- round(runif(size,1,scale),1)
return(result)
}
flag=TRUE
x <- generateRandom(300,6)
y <- generateRandom(300,6)
while(flag){
corrXY <- cor(x,y)
if(corrXY>=0.2){
flag=FALSE
}
else{
x <- generateRandom(300,6)
y <- generateRandom(300,6)
}
}
I want following 6 variables with size 300 and scale of all is between 1 to 6 except for one variable which would have scale 1-7 with following correlation structure among them.
1 0.45 -0.35 0.46 0.25 0.3
1 0.25 0.29 0.5 -0.3
1 -0.3 0.1 0.4
1 0.4 0.6
1 -0.4
1
But when I try to increase threshold value my program gets very slow.Moreover,I want more than 7 variables of size 300 and between each pair of those variables I want some specific correlation threshold.How would I do it efficiently?

Answer 1

This answer is directly inspired from here and there.
We would like to generate 300 samples of a 6-variate uniform distribution with correlation structure equal to
Rhos <- matrix(0, 6, 6)
Rhos[lower.tri(Rhos)] <- c(0.450, -0.35, 0.46, 0.25, 0.3,
0.25, 0.29, 0.5, -0.3, -0.3,
0.1, 0.4, 0.4, 0.6, -0.4)
Rhos <- Rhos + t(Rhos)
diag(Rhos) <- 1
We first generate from this correlation structure the correlation structure of the Gaussian copula:
Copucov <- 2 * sin(Rhos * pi/6)
This matrix is not positive definite, we use instead the nearest positive definite matrix:
library(Matrix)
Copucov <- cov2cor(nearPD(Copucov)$mat)
This correlation structure can be used as one of the inputs of MASS::mvrnorm:
G <- mvrnorm(n=300, mu=rep(0,6), Sigma=Copucov, empirical=TRUE)
We then transform G into a multivariate uniform sample whose values range from 1 to 6, except for the last variable which ranges from 1 to 7:
U <- matrix(NA, 300, 6)
U[, 1:5] <- 5 * pnorm(G[, 1:5]) + 1
U[, 6] <- 6 * pnorm(G[, 6]) + 1
After rounding (and taking the nearest positive matrix to the copula's covariance matrix etc.), the correlation structure is not changed much:
Ur <- round(U, 1)
cor(Ur)