Simulate Correlated data from complex sample

Dear List:

I have created some code to simulate data from a complex sample where
5000 students are nested in 50 schools. My code returns a dataframe with
a variable representing student achievement at a single time point. My
actual code for creating this is below.

What I would like to do is generate a second column of data that is
correlated with the first at .8 and has the same means within each
school. So I do not think I can use mvrnorm or simulate() in the Matrix
package, at least not in a way I can currently see.

A very basic example would be something like first create a vector (s1)
and then generate a second one that is correlated with the first by some
user-defined measure.

s1 <- rnorm(500, 2, 4)

In my example below the variable I want to replicate is data$theta.

I think I could go through the exercise to write code that would so
this, but I think there might be a smarter and easier function for doing
so. I've used RSiteSearch() a bit, but the keywords I'm using aren't
turning up results that I can use. I may be missing something very
simple and transparent.

Any thoughts are much appreciated,
Harold
Ver 2.2
Windows XP


N   <- 5000 # Number of students
J   <- 50   # Number of schools
N_j <- N/J  # Number of students in each school
a_g <- c(0,.5,1) # This is the growth vector

# Step 1 -- create psi for base grade
rps  <- rep(N_j, J)
v_gk <- rep(rnorm(J, 0, sqrt(.01) ), rps)
v_gik <- rnorm(N, 0, sqrt(.99))

# Organize into a dataframe
data  <- data.frame(schid = rep(1:J, rps), stuid = 1:N, cbind(v_gk,
v_gik), psi = v_gk + v_gik  + a_g[1])

# Now create theta
B_g   <- .95 # This is correlation between within-grade trait and
vertical trait
w_gk  <- 0   # fixed at zero for now
data$w_gik <-rnorm(N, 0, sqrt(.0975))
data$theta <- (B_g * data$psi) + w_gk + data$w_gik



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