How is the covariance factor computed?

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

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