Missing values in lmer vs. HLM

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