lme: predictions variance collapses when one more level is added

Dieter Menne <dieter.menne at ...> writes:

Ben Bolker commented:

  Sorry for snipping context here (I'm posting via gmane, which doesn't
like that).  If I use  weights=varIdent(form=~1|treat)) rather than
weights=varPower() (i.e. residual variance varies by treatment group,
rather than as a power function of the estimated mean), I get what
seem (at least at a quick glance) to be reasonable results.

You are right; I received a similar comment from Ariel Muldoon off-list. I
admit that I have tried it, but most have done some stupid syntax mistake so
it go away unnoticed.

While it is a solution, I still do not understand what really happens with
the prediction. And, assuming I am using lmer, what should I do? I noted the
same collapsing effect.

Dieter

I assume that what's going on is just the fairly frequently observed
situation that when the fourth group is included (without invoking
heteroscedasticity), the among-group variation is actually less than
expected from the within-group variation (i.e. less than 
var(within)/(n per group)), implying a negative within-group correlation ...

  I don't think transforming will help here ... David Afshartous
had some postings on allowing different random-effect variances
by treatment groups, but that's not what you need.  We have talked
some about how to implement heteroscedasticity models in lme4, but it's a lot
of work/more or less just a gleam in our eye at this point ...

  Which aspects of lmer are essential in this analysis 
(e.g. profiling, speed, consistency with other analyses, ...?)

  Ben Bolker