[R] repeated measures ANOVA using a cov matrix

[Peter Dalgaard]

sun71 sun wrote:
> Dear all,
> how can I perform a repeated measures ANOVA using a covariance matrix as input?
> E.g., I have four repeated measures (N = 200) with mean vector tau (no
> BS factor):
>
> tau <- rbind(1.10, 2.51, 2.76, 3.52)
>
> and covariance matrix (sigma):
>
> sigma <- matrix(c(0.523, 0.268, 0.267, 0.211,
>                           0.268, 0.444, 0.492, 0.571,
>                           0.267, 0.492, 1.213, 1.112,
>                           0.211, 0.571, 1.112, 1.811), nrow = 4, ncol
> = 4, byrow = TRUE)
>
> Thank you very much in advance!
>
>   
(Please either include new information or wait a little longer for 
someone to react. Reposting after just over a day is a bit like pulling 
on peoples sleeves. And of course you always have the risk that nobody 
has anything to say.)

Your main problem is that few of the standard methods in R allow you to 
come in with pre-aggregated data. So either you have to do it yourself 
using matrix calculus - this is not massively hard if you know what you 
are doing - or you need to fake the raw data and take it from there.

The following generates X2 with variance exactly equal to sigma.  I'm 
sure you can figure out how to get the means right as well.

X <- matrix(rnorm(4*200),200)
X2 <- X %*% solve(chol(var(X))) %*% chol(sigma)

 > var(X2)
      [,1]  [,2]  [,3]  [,4]
[1,] 0.523 0.268 0.267 0.211
[2,] 0.268 0.444 0.492 0.571
[3,] 0.267 0.492 1.213 1.112
[4,] 0.211 0.571 1.112 1.811

(This must be doable with backsolve() too, but the proper incantation 
eludes me just now.)

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>   


-- 
   O__  ---- Peter Dalgaard             Øster Farimagsgade 5, Entr.B
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