[R-sig-ME] Lmer and variance-covariance matrix

[Douglas Bates]

On Fri, Mar 11, 2011 at 2:37 PM, Rolf Turner <r.turner at auckland.ac.nz> wrote:
> 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.)