Re: [R] Simulate Correlated data from complex sample

From: Spencer Graves <spencer.graves_at_pdf.com>
Date: Mon 05 Dec 2005 - 08:10:26 EST

          It may help to recall the following:

          var(X) = var{E(X|School)} + E{var(X|School)}.

          The first term here is the between-group covariance matrix, while the second is the within group covariance matrix. Decide how you want to decompose var(X), and use mvrnorm{MASS} or rmvnorm{mvtnorm} for each, combining them as you've outlined below.

	  Does this make sense?
	  spencer graves

Doran, Harold wrote:

> 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
>
>
>
> [[alternative HTML version deleted]]
>
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-- 
Spencer Graves, PhD
Senior Development Engineer
PDF Solutions, Inc.
333 West San Carlos Street Suite 700
San Jose, CA 95110, USA

spencer.graves@pdf.com
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Received on Mon Dec 05 08:40:42 2005

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