[R-sig-ME] glmer: how are “non-integer #successes in a binomial glm!” actually modeled?

[Bob Wiley]

This is hopefully a clear question but I fear the answer may not be
simple... I have not been able to find anyone who can answer this for me. I
am using the weights= argument in glmer (family = binomial) and get the
non-integer successes warning. I know what this means and why I get it--
some of the weights I have produce values like 4.5 out of 5. This is not an
error, its because on some trials people were awarded partial credit,
essentially.

The estimates of the models seem good to me. And if I round-down or
round-up (i.e. model a 4.5 out of 5 as 4/5 or 5/5) the estimates only
change a little bit. So this makes me confident that whatever lme4 is
doing, it is reasonable. That being said... what IS it doing in these
cases? Should I be doing something other than what I am to model this data,
because of the simple fact that people could receive partial credit on some
trials?

Thanks so much for any help on this confusing issue...

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