heterogeneity in random effects variance

Hi Vito,

I don't think that this functionality exists in lme or lmer right now.
What you describe looks to me as though you'd like to use the varExp
class of functions at the random effects level, instead of at the
within-group level.  The random-effects level has a set of classes for
patterned covariance matrices; the pdMat classes, but this set doesn't
seem to include anything like the varExp class.

So, one thing is that you could write a new pdMat class that provides
the varExp functionality.  I only know vaguely how a person might do
that.  I did a bit of research on writing new varFunc classes but
didn't get enough detail, or have enough time, to start hacking. 
I am happy to share the little that I know if that would be helpful.  

You might also try an EM approach, fitting simpler models within a
loop, using gls and lme alternately, and hoping that it converges.  I
am not sure how that would work right now, but the problem is
interesting, and I'll ponder on it further.  If anyone can suggest how
it might work off the cuff, that would be great!

It is possible that other packages or programs might be able to fit
such models.

Cheers

Andrew

Dear *all*,
(how many.. seeing that this appears to be the first message? :-))

My question concerns LMM and it is not strictly related to developments 
   of the lme4 package.

In a LMM framework is it possible to set a heterogeneity model for the 
random effects? More precisely I am interested in fitting a LMM where 
the random effects:

u~N(0,D(a,b))

where the covariance matrix D is diagonal and depends on two, say, 
parameters a and b to be estimated: D=diag(s1,s2,..,sj,..) and 
sj=exp(a+bxj) with some known values x1,x2,.xj

Is it possible with lmer() (in lme4 package) or even lme() (in nlme 
package)?

I hope to find an answer in this new promising mailing list

Many thanks in advance,

vito


-- 
====================================
Vito M.R. Muggeo
Dip.to Sc Statist e Matem `Vianelli'
Universit? di Palermo
viale delle Scienze, edificio 13
90128 Palermo - ITALY
tel: 091 6626240
fax: 091 485726/485612

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Andrew Robinson  
Department of Mathematics and Statistics            Tel: +61-3-8344-9763
University of Melbourne, VIC 3010 Australia         Fax: +61-3-8344-4599
http://www.ms.unimelb.edu.au/~andrewpr
http://blogs.mbs.edu/fishing-in-the-bay/