[R-sig-ME] Missing values in lmer vs. HLM

[Phillip Alday]

On Sat, 2015-07-04 at 21:21 +0200, Karl Ove Hufthammer wrote:
> Den 04. juli 2015 18:18, Douglas Bates skreiv:
> > Having said all this I will admit that the original sin, the "REML"
> > criterion, was committed by statisticians.  In retrospect I wish that we
> > had not incorporated that criterion into the nlme and lme4 packages but, at
> > the time we wrote them, our work would have been dismissed as wrong if our
> > answers did not agree with SAS PROC MIXED, etc.  So we opted for
> > bug-for-bug compatibility with existing software.
> 
> Hm. I find this statement surprising. I was under the impression REML is 
> *preferred* to ML in many situations (e.g. in simple random intercept 
> models with few observations for each random intercept), and that *ML 
> estimation* may result in severe bias. Do you consider maximising the 
> REML criterion as a bug?
> 

This was my question as well. My understanding was that REML, like
Bessel's correction for the sample variance, was motivated by bias in
the maximum-likelihood estimator for small numbers of observations. The
corrected estimator is in both cases no longer the MLE, so that the ML
part is bit of a misnomer, but if you take "residualized" expansion of
RE instead of "restricted", then REML seems more like a function of ML
and not a "type" of ML.

IIRC, the default in MixedModels.jl is now ML -- have you changed your
opinion about the utility of REML? Is there some type of weird
paradoxical situation with REML like with Bessel's correction -- the
variance estimates are no longer biased, but the s.d. estimates are? 

Or is the original sin the use of the name REML when REML is no longer
*the* maximum likelihood?

Best,
Phillip Alday