[R-sig-ME] lme4: constrain sigma to 0

[Vincent Dorie]

I meant identifiability only in the case of a full mixed model using a residual covariance structure, with variance at the observation and group level. I haven't exactly meditated on it, but you would have a marginal covariance of Sigma_y + Z Sigma_b Z' which could be difficult to identify depending on how things were blocked off.

From what I can tell, the case you're proposing sets Sigma_y to 0, Z to identity, and uses the block repetition of the covariance that goes with the random effects for the observations themselves. I can't speak for the lmer developers, but if I wanted to add that class of models I would do so by adding an extra argument to lmer for the residual variance structure.

Vince

On Feb 13, 2014, at 2:11 PM, Rolf Turner wrote:

> On 14/02/14 09:22, Vincent Dorie wrote:
> 
>> Actually strike what I just said. Identifiability would get in the
>> way more often than not and make it a terrible idea to implement in
>> the general case.
> 
> I don't follow you here.  The problem, it seems to me, is that lmer() insists on fitting an ***unidentifiable*** model, rather than the perfectly legitimate identifiable model that is actually desired.
> 
> It seems to me that the desired model is the basic case of a repeated measures model, whence (it seems to me) it is reasonable to expect to be able to fit it in software for mixed modelling.
> 
> I know it is impolitic to say this on this mailing list, but ``SAS can do it''.  (And without breaking a sweat.)
> 
> cheers,
> 
> Rolf Turner
> 
>> 
>> On Feb 12, 2014, at 7:03 PM, Rolf Turner wrote:
>> 
>>> 
>>> Took me a while, but I have managed to write up some specifics of the problem that I had in mind.  The gremlins seem to have changed things since the last time I played around with this stuff, and what I am now
>>> getting differs from what I recollect.  However there is still a bit of
>>> a problem.
>>> 
>>> I communicated with both Doug Bates and Ben Bolker on this issue, but cannot now for the life of me find any record of the emails that went back and forth.  And I keep ***everything***.  (Always the way; everything but what you want is available.)
>>> 
>>> Anyhow --- I have attached what I hope is a clear write-up in pdf format and a script to demonstrate what goes on using simulated data.
>>> 
>>> I hope these get through ...
>>> 
>>> cheers,
>>> 
>>> Rolf Turner
>>> 
>>> 
>>> On 12/02/14 12:48, Vincent Dorie wrote:
>>> 
>>>> Any chance someone could write out the specifics of such a model? If I
>>> can wrap my head around it and its not too hard, I could try to throw it
>>> into blme.
>>>> 
>>>> On Feb 11, 2014, at 6:18 PM, Rolf Turner wrote:
>>>> 
>>>>> Several millennia ago I put in a feature-request that the facility for
>>>>> constraining sigma to 0 be added. So far, as far as I can tell, it
>>>>> hasn't been.
>>>>> 
>>>>> Apparently it is (very) difficult to add such a constraint due to
>>>>> the way that lmer approaches the maximization of the likelihood.
>>>>> (This, rather than any intrinsic mathematical block to such a
>>>>> constraint.)
>>>>> 
>>>>> I wanted to be able to fit a fairly simple repeated measures model
>>>>> with the covariance over time being an "arbitrary" n-x-n positive
>>>>> definite matrix (where "n" is the number of time points).  This
>>>>> can't be done using lmer() unless one can constrain the "overall"
>>>>> variance to be zero, otherwise the diagonal of the covariance
>>>>> matrix is un-identifiable.
>>>>> 
>>>>> Since one cannot constrain sigma to be 0, one can't fit this model
>>>>> with lmer().  Bummer.
>>> <specifics.pdf><demoScript.txt>
>> 
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>