Between modules, the latent LA factor z's are independent.
Within each module, 10 sub-modules are simulated. For each sub-module, we first generate a pair of X and Y vectors, which follows:
X~N(0,1), Y~N(0,1)
u=(pnorm(z)-0.5)*2
E(XY|z)=sign(u)*abs(u)^pwr
Then white noise with SD of rho is added to the hidden X, Y pair to generate pairs of observed X, Y vectors.