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lmer(): Higher weight in case of more measurements

Despite searching for previous discussions of the issue (which are often
wrestling with more specific questions than the one stated here by
Susanne), I too am confused about how lmer handles it when there is
variation in size among different groups, clusters, or whatever we want to
call levels of a random effect. Maybe I'm using the wrong search terms, but
my efforts seem to reveal that many people are confused by this and - with
the explosion of mixed models in research - are in need of guidance to
prevent serious but simple errors in model specification from being
published. Is there anyone who can give some straightforward guidance on
the issues?

What is the best practice(s) for estimating the effect of an independent
variable in a basic LMM (Y~X + (1|Group)) where the number of data points
varies among the groups?

Thank you in advance to whoever can shed some light!

On Fri, May 15, 2015 at 8:28 AM, Susanne Susanne <susanne.stat at gmx.de>
wrote: