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

[Ben Bolker]

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