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

Jarrod Hadfield j.hadfield at ed.ac.uk
Thu Feb 26 08:00:14 CET 2015

Hi Matthew,

Both MCMCglmm and asreml-r fit these models in R.



  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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