Thank you everyone for the responses.

Vincent's response was very helpful to me (I am not trying to fix sigma to
zero, but to a positive constant).
I would just like to make sure that

blmer(Yield ~ 1|Batch, Dyestuff, cov.prior=NULL, resid.prior = point(SIG))

should be equivalent to what

lmer(Yield ~ 1|Batch, Dyestuff, REML=FALSE)

would give if sigma were restricted to SIG.

Thanks again,
Asaf


On 13 February 2014 07:22, Viechtbauer Wolfgang (STAT) <
wolfgang.viechtbauer@maastrichtuniversity.nl> wrote:

> 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@r-project.org [
> r-sig-mixed-models-bounces@r-project.org] On Behalf Of Rolf Turner [
> r.turner@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.
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