[R-sig-ME] Random-effects variance-covariance matrix in lmer?

[Phillip Alday]

On 02/10/2019 16:52, matthias.suter using agroscope.admin.ch wrote:
> Thanks, Philipp.
> 
> I was a aware of the pdDiag and the pdCorSym solution, and so I specifically asked for pdCompSym and pdIdent ...
> 
> As for your compound symmetry suggestion, it is not quite clear to me. Up to now, I would have named "(1|Worker:Machine)" a random interaction term, specifying a distinct level for each worker*machine combination (and that's what is given by ranef(m_cs). How does this relate to the covariance in the compound symmetry, where also a multiple of identity is fit to diagonal?

I stole this example from an old presentation of Doug Bates:

http://pages.stat.wisc.edu/~bates/UseR2008/WorkshopD.pdf

This is one of those things that my uni math instructors used to say
"Convince yourself this is true". I hated it at the time, but I don't
have the time to think about how to articulate this better than
"thinking about what is being allowed in terms of geometry". Sorry. :(

> 
> I have also tried to sort out the pdIdent equivalent, using similar coding as you suggest below, but was not successful so far. Do you know a similar solution?

I don't off the top of my head. pdIdent really isn't relevant to my day
job so I don't think about it much. I think it might be relatively
straightforward to do in MixedModels.jl via something similar to the new
zerocorr! function in the dev version, but it's not a priority for me.
Pull-requests always welcome. (Slightly higher but still not terribly so
on my priority list is documenting the internal fields of ReMat
structure to make the logic of such modifications somewhat more obvious.)

Phillip

> Thanks again,
> Matthias 
> 
> 
> 
> 
> -----Ursprüngliche Nachricht-----
> Von: Phillip Alday <phillip.alday using mpi.nl> 
> Gesendet: Mittwoch, 2. Oktober 2019 16:30
> An: Suter Matthias Agroscope <matthias.suter using agroscope.admin.ch>; r-sig-mixed-models using r-project.org
> Betreff: Re: [R-sig-ME] Random-effects variance-covariance matrix in lmer?
> 
> This is a frequent question for lme4 and MixedModels.jl and the answer is....
> 
> it's not going to be supported in any mainstream release of either package in the foreseeable future.
> 
> You can however still get some of these structures by clever specification of the random effects.
> 
> For example:
> 
> data(Machines,package="nlme")
> library(lme4)
> 
> m <- lmer(score ~ 1 + Machine + (0+Machine|Worker), Machines)
> 
> # with compound symmetry
> m_cs <- lmer(score ~ 1 + Machine + (1|Worker) + (1|Worker:Machine),
> Machines)
> 
> # pdDiag -- for continuous variables, you could just use the || syntax
> 
> m_diag <- lmer(score ~ 1 + Machine + (0+dummy(Machine,"A")|Worker) +
> (0+dummy(Machine,"B")|Worker) + (0+dummy(Machine,"C")|Worker), Machines)
> 
> I'll leave pdIdent as an exercise for the OP. ;)
> 
> Best,
> Phillip
> 
> On 02/10/2019 15:50, matthias.suter using agroscope.admin.ch wrote:
>> Hi all
>>
>> I'm looking for a way to specify a more complex variance-covariance matrix for the random effects in lmer(). For example, in lme() (nlme package), there are the pdMat classes to specify e.g. a compound symmetry (pdCompSym) or a multiple of an identity (pdIdent) structure for the variance-covariance matrix of random effects. Is there a possibility to code an equivalent for lmer()? I'm specifically interested in "compound symmetry" and "multiple of an identity".
>>
>> I assume that Douglas Bates or Ben Bolker have a distinct answer on that.
>>
>> Thanks in advance,
>> Matthias
>>
>>
>> ---------------------------------------------------------
>> Matthias Suter, Dr.sc.nat.
>> Forage Production and Grassland Systems
>>
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>>
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