estimating variance components for arbitrarily defined var/covar matrices

-----Original Message-----
From: Jarrod Hadfield [mailto:j.hadfield at ed.ac.uk]
Sent: Thursday, February 26, 2015 17:42
To: Viechtbauer Wolfgang (STAT)
Cc: r-sig-mixed-models at r-project.org; Matthew Keller
Subject: Re: [R-sig-ME] estimating variance components for arbitrarily
defined var/covar matrices

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!