基于Winbugs / JAGS脚本在R中模拟多元分布中的数据

Question

I am trying to simulate data, based on part of a JAGS/Winbugs script. The script comes from Eaves & Erkanli (2003, see, http://psych.colorado.edu/~carey/pdffiles/mcmc_eaves.pdf , page 295-296).

The (part of) the script I want to base my simulations on is as follows (different variable names than in the original paper):

 for(fam in 1 : nmz ){
    a2mz[fam, 1:N] ~ dmnorm(mu[1:N], tau.a[1:N, 1:N])
    a1mz[fam, 1:N] ~ dmnorm(a2mz[fam, 1:N], tau.a[1:N, 1:N])
 }

 #Prior
 tau.a[1:N, 1:N] ~ dwish(omega.g[,], N) 

I want to simulate data in R for the parameters a2mz and a1mz as given in the script above.

So basically, I want to simualte data from -N- (eg = 3) multivariate distributions with -fam- (eg 10) persons with sigma tau.a.

To make this more illustrative: The purpose is to simulate genetic effects for -fam- (eg 10) families. The genetic effect is the same for each family (eg monozygotic twins), with a variance of tau.a (eg 0.5). Of these genetic effects, 3 'versions' (3 multivariate distributions) have to be simulated.

What I tried in R to simulate the data as given in the JAGS/Winbugs script is as follows:

 library(MASS)
 nmz = 10 #number of families, here e.g. 10
 var_a = 0.5 #tau.g in the script

 a2_mz <- mvrnorm(3, mu = rep(0, nmz), Sigma = diag(nmz)*var_a)

This simulates data for the a2mz parameter as referred to in the JAGS/Winbugs script above:

 > print(t(a2_mz))
        [,1]       [,2]        [,3]
  [1,] -1.1563683 -0.4478091 -0.15037563
  [2,]  0.5673873 -0.7052487  0.44377336
  [3,]  0.2560446  0.9901964 -0.65463341
  [4,] -0.8366952  0.4924839 -0.56891991
  [5,]  0.7343780  0.5429955  0.87529201
  [6,]  0.5592868 -0.3899988 -0.33709105
  [7,] -1.8233663 -0.7149141 -0.18153049
  [8,] -0.8213804 -1.4397075 -0.09159725
  [9,] -0.7002797 -0.3996970 -0.29142215
  [10,]  1.1084067  0.3884869 -0.46207940 

However, when I then try to use these data to simulate data for the a1mz (third line of the JAGS/Winbugs) script, then something goes wrong and I am not sure what:

 a1_mz <- mvrnorm(3, mu = t(a2_mz), Sigma = c(diag(nmz)*var_a, diag(nmz)*var_a,     diag(nmz)*var_a))

This results in the error: Error in eigen(Sigma, symmetric = TRUE, EISPACK = EISPACK) : non-square matrix in 'eigen'

Can anyone give me any hints or tips on what I am doing wrong?

Many thanks, Best regards, inga

Answer 1

mvrnorm() takes a mean-vector and a variance matrix as input, and that's not what you're feeding it. I'm not sure I understand your question, but if you want to simulate 3 samples from 3 different multivariate normal distributions with same variance and different mean. Then just use:

a1_mz<-array(dim=c(dim(a2_mz),3))
for(i in 1:3)  a1_mz[,,i]<-mvrnorm(3,t(a2_mz)[,i],diag(nmz)*var_a)