[R] Fitting mixed-effects models with lme with fixed error term variances

[Gregor Gorjanc]

Hello!

Douglas Bates wrote:
...
>> > Not quite.  There is now a capability in lmer to specify starting
>> > estimates for the relative precision matrices which means that you can
>> > use the estimates from one fit as starting estimates for another fit.
>> > It looks like
>> >
>> > fm1 <- lmer(...)
>> > fm2 <- lmer(y ~ x + (...), start = fm1 at Omega)
>> >
>> > I should say that in my experience this has not been as effective as I
>> > had hoped it would be.  What I see in the optimization is that the
>> > first few iterations reduce the deviance quite quickly but the
>> > majority of the time is spent refining the estimates near the optimum.
>> > So, for example, if it took 40 iterations to converge from the rather
>> > crude starting estimates calculated within lmer it might instead take
>> > 35 iterations if you give it good starting estimates.
>>
>> Yes, I also have the same experience with other programs, say VCE[1].
>> What I was hopping for was just solutions from linear mixed model i.e.
>> either via GLS or PLS representations and no optimization if values for
>> variance components are passed as input - there should be a way to
>> distinguish that from just passing starting values..
> 
> The PLS representation in lmer is in terms of the relative
> variance-covariance matrices of the random effects where "relative"
> means relative to s^2.  (In fact, the Omega slot contains the relative

What exactly is s^2?

> precision matrices (inverses of the relative variance matrices) but
> its the same idea.  All variance components are expressed relative to
> s^2.)  If it is sufficient to fix these then you can easily do that.
> Just follow the code in lmer until it gets to
> 
>   .Call(mer_ECMEsteps, mer, cv$niterEM, cv$EMverbose)
>   LMEoptimize(mer) <- cv
>   return(new("lmer", mer,
> 
> and replace the first two lines by
> 
>   .Call("mer_factor", mer, PACKAGE = "lme4")

Hmm. Sounds simple. I will try this. Do you find any value in adding
this as an option in lmer or perhaps new? function, say lmeSol() or
something similar?

> A side-effect of performing the factorization is to evaluate the ML
> and REML deviances and store the result in the deviance slot.
> 
> The "follow the code in lmer" part will get a bit tricky because of
> the number of functions that are hidden in the lme4 namespace but I'm
> sure you know how to get around that.

Thank you very much!

Gregor