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

Rolf Turner r.turner at auckland.ac.nz
Thu Feb 26 02:07:16 CET 2015

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.



On 26/02/15 13:12, Ben Bolker wrote:
> Hash: SHA1
>    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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Rolf Turner
Technical Editor ANZJS
Department of Statistics
University of Auckland
Phone: +64-9-373-7599 ext. 88276
Home phone: +64-9-480-4619

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