How to constrain varcov of 2 random effects so that correlation between random terms is 1 and only one global variance is estimated?

Hi Alexandre,

It sounds like you want to fit something called a multi-membership  
model.  Imagine a data set set out like:

y  A  B

1  a  b
0  a  c
2  c  b
0  b  a
3  a  d

you want the effect of a in A to equal the effect of a in B, such that  
the random effect model for the 1st and 4th row are identical. Is this  
correct?

If so the covariance matrix for the random effects should actually be  
[V,V,V,V] rather than [V,1,1,V].

I'm not sure if multi-membership models can be fitted in lmer but some  
earlier posts suggest not. In MCMCglmmm you can fit this model by  
fitting

random=~idv(mult.memb(~A+B))

Note that this only fits a single variance V.  A and B have to be  
factors with the same levels, although it is not necessary that all  
levels are represented in each factor. In the example above, d only  
appears in B, but the analysis will still work as long as d is a level  
in A. i.e. factor(A, levels=union(A,B)).

The initial set up may be slow because the design matrices are not  
treated as sparse, but once it is MCMCing in C++ it is working with  
sparse matrices and should be relatively speedy.

Cheers,

Jarrod








Quoting Alexandre Courtiol <alexandre.courtiol at gmail.com>:

Dear all,
I need to do a linear mixed model and I want to constrain the varcov matrix
of random effects. Let's say I have 2 random effects A and B, I want the
matrix to be [V,1,1,V], i.e. V=VA=VB, and 1=cor(A,B). Both random effects
are factors with the same levels. Is there any easy way to do that in lme,
lmer, mcmcglmm or something else? (I don't care so much about the package to
use as long as I can do that).
Thanks a lot.

--
Alexandre Courtiol

http://sites.google.com/site/alexandrecourtiol/home

	[[alternative HTML version deleted]]

_______________________________________________
R-sig-mixed-models at r-project.org mailing list
https://stat.ethz.ch/mailman/listinfo/r-sig-mixed-models

The University of Edinburgh is a charitable body, registered in
Scotland, with registration number SC005336.