Lmer and variance-covariance matrix

On 12/03/11 02:56, Jarrod Hadfield wrote:

Hi,

In addition, each trait is only measured once for each id (correct?)
which means that the likelihood could not be optimised even if the
data-set was massive. If you could fix the residual variance to some
value (preferably zero) then the problem has a unique solution given
enough data, but I'm not sure this can be done in lmer?.

<SNIP>

I think that it ***CANNOT*** be done. ?I once asked Doug about
the possibility of this, and he ignored me. ?As people so often
do. :-) Especially when I ask silly questions .....

Did Doug really ignore you or did he say that the methods in lmer are
based on determining the solution to a penalized linear least squares
problem so they can't be applied to a model that has zero residual
variance.  Also the basic parameterization for the variance-covariance
matrix of the random effects is in terms of the relative standard
deviation (\sigma_1/\sigma) which is problematic when \sigma is zero.

(My apologies if I did ignore you, Rolf.  I get a lot of email and
sometimes such requests slip down the stack and then get lost.  I'm
very good at procrastinating about the answers to such questions.)