[R-sig-ME] estimating variance components for arbitrarily defined var/covar matrices

[Jarrod Hadfield]

Hi,

If the `genetic' matrix is pedigree derived (?) the matrix is a  
correlation matrix (in the absence of inbreeding) or proportional to  
the covariance matrix (with inbreeding). However, the matrix has a lot  
of structure that can be exploited by *not* treating it as just  
another correlation matrix. Specifically, the inverse of the matrix is  
all zeros, except for the diagonal elements and those that correspond  
to mates and/or parent-offspring. ASReml, WOMBAT, MCMCglmm, pedigreem  
(?) + others all exploit this structure leading to faster more robust  
results. For small problems this might not be an issue.

Cheers,

Jarrod



Quoting "Viechtbauer Wolfgang (STAT)"  
<wolfgang.viechtbauer at maastrichtuniversity.nl> on Thu, 26 Feb 2015  
17:24:39 +0100:

> And just to throw another package in the mix, you can also use the  
> metafor package for this. While this doesn't quite sound like a  
> meta-analysis, in the end, meta-analysis models are just  
> mixed-effects models. And in a phylogenetic meta-analysis, we add  
> random effects with known correlations matrices to the model.
>
> The syntax would be:
>
> id.e <- 1:nrow(dat)
> id.r <- 1:nrow(dat)
> rma.mv(y ~ <fixed effects>, V = 0, random = list(~ 1 | id.r, ~ 1 |  
> id.e), R = list(id.r = GRM), data=dat)
>
> where 'GRM' is the n x n matrix of similarities. The V = 0 part  
> seems a bit strange, but in meta-analytic models, we usually don't  
> estimate the error variance and instead have known sampling  
> variances (or even a known variance-covariance matrix of the  
> sampling errors). Here, we don't, so we just set that part to 0  
> (you'll get a warning that 'V appears to be not positive definite.'  
> but you can safely ignore this). This will fit the model that you  
> specified below.
>
> Besides the estimates of the fixed effects, the results will include  
> two variance components, one for id.r (this is VG) and one for id.e  
> (this is sigma^2_error). The default is REML estimation (method="ML"  
> is you want MLEs).
>
> By default, rma.mv() tries to rescale the matrix supplied via the R  
> argument into a correlation matrix. Not sure if your matrix of  
> similarities is really a correlation matrix or not. In case you  
> don't want the function to mess with the matrix, set 'Rscale=FALSE'  
> and it won't touch it.
>
> Best,
> Wolfgang
>
> --
> Wolfgang Viechtbauer, Ph.D., Statistician
> Department of Psychiatry and Psychology
> School for Mental Health and Neuroscience
> Faculty of Health, Medicine, and Life Sciences
> Maastricht University, P.O. Box 616 (VIJV1)
> 6200 MD Maastricht, The Netherlands
> +31 (43) 388-4170 | http://www.wvbauer.com
>
>> -----Original Message-----
>> From: R-sig-mixed-models [mailto:r-sig-mixed-models-bounces at r-
>> project.org] On Behalf Of Anthony R Ives
>> Sent: Thursday, February 26, 2015 13:04
>> To: Jarrod Hadfield; Matthew Keller
>> Cc: r-sig-mixed-models at r-project.org
>> Subject: Re: [R-sig-ME] estimating variance components for arbitrarily
>> defined var/covar matrices
>>
>> Matthew,
>>
>> You should be able to do this in communityPGLMM in {pez}. Also, Steve
>> Walker is currently working on a way to do this in lmer/glmer.
>>
>> Cheers, Tony
>>
>>
>> On 02/26/15, Jarrod Hadfield  wrote:
>> > Hi Matthew,
>> >
>> > Both MCMCglmm and asreml-r fit these models in R.
>> >
>> > Cheers,
>> >
>> > Jarrod
>> >
>> > Quoting Matthew Keller <mckellercran at gmail.com> on Wed, 25 Feb 2015
>> 16:42:32 -0700:
>> >
>> > >Hi all,
>> > >
>> > >This is a typical problem in genetics and I'm trying to figure out
>> whether
>> > >there's any way to solve it using lmer or similar, and if not, why it
>> isn't
>> > >possible.
>> > >
>> > >Often in genetics, we have an n-by-n matrix (n=sample size) of genetic
>> > >relationships, where the diagonal is how related you are to yourself
>> (~1,
>> > >depending on inbreeding) and off-diagonals each pairwise relationship.
>> I'd
>> > >like to be able to use lmer or some other function in R to estimate
>> the
>> > >variance attributable to this genetic relationship matrix. Thus:
>> > >y = b0 + b*X + g*Z + error
>> > >where y is a vector of observations, b is a vector of fixed covariate
>> > >effects and g is a vector of random genetic effects. X and Z are
>> incidence
>> > >matrices for b & g respectively, and we assume g ~ N(0, VG). The
>> variance
>> > >of y is therefore
>> > >var(y) = Z*Z' * VG + I*var(e)
>> > >
>> > >Z*Z' is the observed n-by-n genetic relationship matrix. Given an
>> observed
>> > >Z*Z' genetic relationship matrix, is there a way to estimate VG?
>> > >
>> > >I guess this boils down to, if we have an observed n-by-n matrix of
>> > >similarities, can we use mixed models in R to get the variance in y
>> that is
>> > >explained by that similarity?
>> > >
>> > >Thanks in advance!
>
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