It would be nice to be able to fix the residual variance (sigma) to 1, 
so meta-analyses can be performed with lme4. Maybe this is hard to 
implement though.

Gustaf

> On 03/11/2011 05:11 PM, Rolf Turner wrote:
>> >  On 12/03/11 09:45, Douglas Bates wrote:
>>> >>  On Fri, Mar 11, 2011 at 2:37 PM, Rolf Turner<r.turner@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.)
>> >  
>> >  Yes, you really did ignore me.  But not to worry; I'm used to it!:-)
>> >  I also (more recently) asked Ben Bolker about this issue.  He
>> >  ignored me too!  At that stage I kind of took the hint ......
>> >  
>    I want to distinguish two cases here.
>    It would be reasonable (although I think not currently feasible) to
> fix any variance parameter*other than the residual variance*  to zero,
> refitting the model with that constraint, to do a test of the effect of
> that parameter (keeping in mind the various limitations of finite sample
> sizes/unknown null distributions, testing on the boundary, blah blah
> blah).  This is a special case of the machinery that has to be built in
> order for profiling of the random effects to work, and at a pinch you
> can get the answer (if you can get lme4a to run on your system) by
> fitting the profile and looking at the value at the boundary.
>    It is reasonable, but not within the framework of lme4, to set one
> particular random effect -- the residual variance -- to zero, because
> (as Doug points out) it has a special role.
>
>    cheers
>      Ben Bolker
>
>
>> >  Your explanation of why it can't be done makes perfect sense.
>> >  
>> >  However I find this constraint sad, because I like to be able to
>> >  fit ``marginal case'' models, which can also be fitted in a more
>> >  simple-minded manner and compare the results from the
>> >  simple-minded procedure with those from the sophisticated
>> >  procedure.  If they agree, then this augments my confidence
>> >  that I am implementing the sophisticated procedure correctly.
>> >  
>> >  An example of such, relating to the current discussion, is a
>> >  simple repeated measures model with K (repeated) observations
>> >  on each of N subjects, with the within-subject covariance matrix
>> >  being an arbitrary positive definite K x K matrix.
>> >  
>> >  This could be treated as a mixed model (if it were possible to
>> >  constrain the residual variance to be 0).  It can also be treated
>> >  as a (simple-minded) multivariate model --- N iid observations
>> >  of K-dimensional vectors, the mean and covariance matrix of
>> >  these vectors to be estimated.
>> >  
>> >  I would have liked to be able to compare lmer() results with the
>> >  (trivial) multivariate analysis estimates.  To reassure myself that
>> >  I was understanding lmer() syntax correctly.
>> >  
>> >       cheers,
>> >  
>> >           Rolf

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