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

[Steve Walker]

Thanks Tony.  For those interested, you can check out the development of 
my work on phylogenetic models in lme4 here:

https://github.com/stevencarlislewalker/lme4ord

The section in the README file about phylogenetic models gives an 
example and briefly describes the kinds of models that can be fitted.

Regarding speed, the glmerc (with a 'c' for known covariance over 
grouping factor levels) function can fit models similar to the one in 
the README but with a 500 tip phylogeny in about 20 seconds on my pretty 
standard macbook pro.  lme4 uses sparse matrices for all random 
effect-related matrix computations, so most of the speed comes from this 
infrastructure.  However, it may be possible to speed things up more by 
exploiting Kronecker-product-type structure, but this would require some 
substantial additions to lme4, I think.

I should also note that the models fitted by glmerc do _not_ allow for 
fitting parameters that scale branch lengths (e.g. Ornstein-Uhlenbeck). 
  The fundamental challenge with these models in lme4 is that lme4 is 
based on a Cholesky factor parameterization of the random effects 
covariance matrix.  To parameterize the covariance matrix on the 
covariance or branch length scale, one would need to compute a Cholesky 
factor every time the deviance function is evaluated.  This could get 
costly.  The recent methods of Ho and Ané (2014) in the phylolm package 
might help here.  However, in their current form these methods only 
apply to quadratic terms involving the inverse covariance matrix and to 
the log determinant of the covariance matrix.  These computations are 
certainly important in mixed modelling in general, but unfortunately not 
_so_ much for lme4, because of the Cholesky parameterization.  However, 
I bet that their ideas could be modified to be applicable to lme4.  In 
particular I bet one could compute a series of small Cholesky 
decompositions at the tips and then iteratively rank-one update them by 
traversing the tree to the root.  My guess is that this procedure would 
scale linearly, as do the other methods of Ho and Ané (2014).

Cheers,
Steve

On 2015-02-26 7:04 AM, Anthony R Ives wrote:
> 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!
>>>
>>> [[alternative HTML version deleted]]
>>>
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>>>
>>>
>>
>>
>>
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