I am sorry for the misleading title of my mail. I didn't want to
discuss the utility of having LRT tests done with REML versus not
REML estimates, I think this doesn't deserve much discussion (i.e.,
REML + LRT = bad).
The point I wanted to make is just that it is relatively uncommon
that an anova method is time consuming (which it may be in case of
refit) and furthermore it is somewhat unsatisfactory that anova does
not allow to pass the really nice control options to the
optimizer. Obviously one can simply circumvent this issue by fitting
the model directly with lmer and REML = FALSE and pass the correct
optimizer arguments and then use this model as argument to anova.
However, the optimization envoked by refit may also fail to converge
in the number of default maxfun steps simply if there are many
observations. This does not need to be due to a misspecified
model. In fact in my real data, the warning message said exactly
this (and came through anova): "maxfun < 10 * length(par)^2 is not
recommended". And there is no way to change maxfun if refit is
envoked.
Hence my pledge for a warning instead of calling refit automatically.
Best,
Henrik
PS: I realize that this problem only appeared because I stupidly
tried to compare to REML LMMs with anova which I shouldn't have
done...