I am wanting to generate a dataset of $N = 1,000,000$ simulated examinees according to the following constraints:
- All 1e6 take a battery of 10 subtests
- All 10 of the subtests have a population mean of 100 and a population standard deviation of 15
- All of the subtests have a correlation matrix of $\mathbf S$
- The within-person scatter from one subtest to another follows a normal distribution with mean = $M$ and standard deviation $\sigma$
In R, there are commands that will sample multivariate distributions that obey a particular correlation matrix. But is there any command or library that will sample multivariate distributions according to the parameters I have listed above?