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

[Viechtbauer Wolfgang (STAT)]

Is there a particular reason why you would want to fit this with lmer() as opposed to gls() from nlme? In your demo script:

res <- gls(y ~ time, correlation = corSymm(form = ~ 1 | student), weights = varIdent(form = ~ 1 | time), data=dat.sim)

will fit that model.

Best,
Wolfgang
________________________________________
From: r-sig-mixed-models-bounces at r-project.org [r-sig-mixed-models-bounces at r-project.org] On Behalf Of Rolf Turner [r.turner at auckland.ac.nz]
Sent: Thursday, February 13, 2014 1:03 AM
To: Vincent Dorie
Cc: r-sig-mixed-models
Subject: Re: [R-sig-ME] lme4: constrain sigma to 0

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.