[R-sig-ME] How is the covariance factor computed?

[Vincent Dorie]

> (I
> think "... the sigma parameters are then simply numerically optimized"
> should be "... the theta parameters ...")


Whoops. Ben is right, as usual.

On Jul 17, 2014, at 4:18 PM, Ben Bolker <bbolker at gmail.com> wrote:

> Vincent Dorie <vdorie at ...> writes:
> 
> [snip]
> 
>> On the other hand, if you were asking where those numbers come from,
>> it turns out that (at least for linear models) those parameters are
>> sufficient to define a likelihood wherein the fixed effects and
>> conditional error term (sigma) are analytically optimized. Since the
>> goal is a maximum likelihood, or REML, the sigma parameters are then
>> simply numerically optimized. You can then easily evaluate the mixed
>> model likelihood at any value of the var/cov matrix of the random
>> effects that you like, provided you are willing to accept maximal
>> values for the fixed effects and sigma. If you wanted to plug those
>> values in as well, it's a bit of a pain but it can be done.  
>>  Vince
> 
>  ... specifically, for this last bit, see the devfun2() function in
> https://github.com/lme4/lme4/blob/master/R/profile.R ; there is a
> brief description of how this works in the lme4 preprint at
> http://arxiv.org/abs/1406.5823 , in the 'profiling' section.  (I
> think "... the sigma parameters are then simply numerically optimized"
> should be "... the theta parameters ...") [defined in previous para.
> as the elements of the Cholesky factorization(s) of the random effects
> variance-covariance matri[xc](es) ...]
> 
>  Ben Bolker
> 
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