[R-sig-ME] MCMCglmm: Within- versus between-individual covariances

[Jarrod Hadfield]

Hi Ned,

Currently it is not possible to specify covariance matrices with  
arbitrary covariances set to zero. If you can reorder the terms so  
that the covariance matrix has a block structure (eg swap trait 2 and  
3 in your example) then you can fit this is in the random terms.  
However, the residual term can only be specified by a single term so  
this is not possible. You can still run the model with a us structure  
of course, but as you are aware the posterior distribution for the  
non-identified covariances will simply be the prior distribution.

Cheers,

Jarrod

Quoting Ned Dochtermann <ned.dochtermann at gmail.com>:

> I tried to find an answer to this problem but either failed to select the
> proper search terms or this topic hasn't been discussed. I apologize if the
> former. I've also consulted the "class notes" for MCMCglmm but that hasn't
> clarified the issue for me.
>
> I am currently working on the analysis of some repeated measures behavioural
> data and am attempting to estimate variances and covariances among
> behaviours. Specifically we're looking to estimate the between-individual
> (co)variance matrix and I was using a multi-response model and the Poisson
> family in MCMCglmm to do so.
>
> I had thought that the posterior modes for the (co)variance matrix (i.e.
> posterior.modes(model$VCV)) was producing this on the latent scale, with the
> ".ID" terms being the between individual (co)variances and the ".unit" terms
> being the within/residual indvidual (co)variances. This conclusion was based
> on Jarrod Hadfield's appendix to the recent animal model paper published in
> the Journal of Animal Ecology (2009). In the appendix discussing MCMCglmm
> for repeated measures, repeatability is calculated using the .ID variance as
> the between individual component and the .unit variance as the within
> individual component.
>
> The problem I've encountered is that due to the experimental design certain
> aspects of the within individual covariance matrix should not be
> estimatable, but estimates are nonetheless reported. This is, of course, due
> to my misspecification of the model.
>
> To use an example provided by a colleague, consider a situation where three
> distinct behaviours are measured and we're interested in their covariance.
> Due to aspects of the experimental manipulation all the behaviours cannot be
> measured on the same days. Thus the data might look something like:
>
> ID	Day	Behav1	Behav2	Behav3
> 1	1	4		NA		10
> 1	2	3		NA		15
> 1	3	NA		5		NA
> 1	4	NA		4		NA
> 2	1	2		NA		12
> 2	2	1		NA		18
> 2	3	NA		4		NA
> 2	4	NA		3		NA
> ...
> N	1	6		NA		8
> N	2	5		NA		6
> N	3	NA		8		NA
> N	4	NA		7		NA
> [[note, I know these fictitious data aren't necessarily Poisson distributed
> but the actual data are]]
>
> In this case between individual variances and covariances can be calculated
> among all three behaviours and within individual covariances should be
> calculated between Behav1 and Behav3 but not for Behav2 with either 1 or 3
> due to separation.
>
> In attempting the initial analyses I specified the random statement using an
> unstructured matrix:
>> random=~us(trait):ID
> (I'm pretty sure that's what I want and what produces the between individual
> covariance matrix)
>
> I also kept the residual covariance matrix as the default unstructured:
>> rcov=~us(trait):units
>
> However, if the within-individual/residual covariances really shouldn't be
> calculated between Behav2 and the other two responses, rcov should actually
> look something like:
>
> v.B1		0		cov.B1*3
> 0		v.B2		0
> cov.B1*3	0		v.B3
>
> For this example "~us" is thus estimating two extra parameters that
> shouldn't be estimated (for the actual dataset these elements have
> credibility intervals overlapping 0).
>
> Clearly idh wouldn't be appropriate for this either but none of the options
> listed in Table 3.1 of the Class Notes for MCMCglmm seem correct. It also
> doesn't look like I can specify the matrix structure directly (which is how
> my colleague dealt with this concern using ASreml and which I know SAS
> allows for regular mixed models).
>
> Is there any advice on how best to deal with this issue? I'm at a loss.
>
> Thanks a lot,
> Ned Dochtermann
>
>
> --
> Ned Dochtermann
> Department of Biology
> University of Nevada, Reno
>
> ned.dochtermann at gmail.com
> http://wolfweb.unr.edu/homepage/mpeacock/Dochter/
> --
>
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>



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