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

Ben Bolker bbolker at gmail.com
Thu Feb 26 04:54:20 CET 2015

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  I thought we were assuming a fixed var-cov matrix PLUS an error
variance, i.e. Sigma + s^2*I (increasing the variance and decreasing
the correlation).

  But I could be wrong about what model is intended.

On 15-02-25 08:07 PM, Rolf Turner wrote:
> Ben:  Perhaps I am misunderstanding, but isn't this essentially the
> same as a problem that I asked you about, some years ago, about
> which you said that it cannot currently be done in lme4?
> I guess that in my old question to you, Z*Z' was the identity
> matrix, so the current question is perhaps a generalization of my
> question.
> The catch, it seems to me, is that var(e) is ill-defined --- you
> can replace var(e) by var(e) - zeta and Z*Z*VG by Z*Z'*VG + zeta*I
> for any zeta such that
> -delta < zeta < var(e)
> where delta = min(diag(Z*Z'*VG)), and have an equivalent model.
> Is it not so?  If not, what am I misunderstanding?
> In my question to you I asked if one could constrain var(e) to be
> zero so as to make the model well defined, and you said no, one
> could not, because of the way lmer does its estimation.
> cheers,
> Rolf
> On 26/02/15 13:12, Ben Bolker wrote: I haven't actually tried any
> problems like this, but
> 1. in principle this is possible 2. There's a hack at 
> http://stackoverflow.com/questions/19327088/reproducing-results-from-previous-answer-is-not-working-due-to-using-new-version/19382162#19382162
>  3. you might take a look at the pedigreemm package for another 
> example.  There *might* be something else in the Reverse 
> Depends/Suggests list at 
> http://cran.r-project.org/web/packages/lme4/index.html , but
> nothing jumps out at me.
> Steve Walker is in the very early stages of working on a 
> phylogenetic model with a similar structure.
> Looking forward to seeing what other people have to say ...
> Ben
> On 15-02-25 06:42 PM, Matthew Keller wrote:
>>>> 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!
>>>> [[alternative HTML version deleted]]
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