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    $\begingroup$ +1. I agree with what you say. As I mentioned in my original post : "over-dispersion (...) is how you "get around" the issue of having as many groups as observations." Thank you for making a better point of glmer in a conceptual manner. $\endgroup$ Commented Jul 24, 2013 at 22:08
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    $\begingroup$ Thanks for the links! After reading those, and having a closer look at the fitted values from my model, I have a better idea of what's going on. I actually don't think what Ben is doing is appropriate for my analysis. He's using an observation-level variable to allow for overdispersion, so it's like a nuisance effect. For my analysis, distributor is an effect of interest: I want to see how distributors perform relative to each other when allowing for other variables. Thus it's more comparable to a conventional linear mixed model, where overfitting is a genuine concern. $\endgroup$ Commented Jul 25, 2013 at 7:24