[R] Nested variance-covariance matrix in Multilevel model
Tobias Guennel
tguennel at vcu.edu
Mon Jun 19 22:06:37 CEST 2006
Dear R community,
I have trouble implementing a nested variance-covariance matrix in the
lme function.
The model has two fixed effects called End and logpgc, the response
variable is the logarithm to base 2 of Intensity ( log2(Intensity) )
and the random effects are called Probe and ProbeNo.
The model has the following nesting structure: A Pixel is nested within
the ProbeNo,the ProbeNo is within the ProbeEnd ( there are two ends for
every probe), and the ProbeEnd is within the Probe.
Now the problem I have is that the variance-covariance structure of the
model is quite complex and I can not find the right syntax for fitting
it in the lme function.
The variance-covariance structure is a block diagonal matrix of the form,
V1 0 0
V= 0 V2 0
0 0 V3
where V1...V3 are of the structure:
v11 v12
V1= and so on.
v21 v22
V1...V3 are assumed to have a compound symmetric variance-covariance
structure and therefore the submatrices are of the form:
Lambda Delta1 Delta1 ... Delta1
Delta1 Lambda Delta1 ... Delta1
v11=v22= .......
Delta1 ..... Lambda
Delta2 Delta2 Delta2 ... Delta2
Delta2 Delta2 Delta2 ... Delta2
v12=v21= .......
Delta2 ..... Delta2
The elements of these submatrices depend only upon the three covariance
parameters: the compound symmetry parameter delta; the variance of
random effect sigma^2g; and the residual variance sigma^2. I have
formulas for the submatrices Lambda,Delta1 and Delta2 which I can't
really paste in here.
The SAS code dealing with this model is the following:
proc mixed data=rnadeg.pnau;
title 'CV structure for PNAU';
class probepos probeno end probe pixelid newprobeid;
model logPM=end logpgc / ddfm=satterth;
random probeno newprobeid / subject=probe type=cs;
lsmeans end / diff cl; run;
Any ideas are appreciated a lot since I am kind of stuck at this point.
Thank you
Tobias Guennel
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