[R-sig-ME] How to Model U-Shaped Distribution in LME4

[David Jones]

I am looking at medication adherence as a DV. I am having difficulty
considering how to model adherence in LME4, as the distribution is very
u-shaped.

In particular, the distribution is bimodal - participants usually
didn't adhere at all, or adhered completely (30% of responses did not
adhere at all, while 55% of responses had full adherence, despite it
being measured on a ratio scale). Q-Q and P-P plots also reflect
problems with modeling adherence as Gaussian.

I was wondering what thoughts would be regarding the best distribution
to apply to this variable - beta binomial has been mentioned, and I
was wondering if other options come to mind that are available in
LME4.

Of note, as it has turned out there have only been 8 response
categories despite adherence being a continuous measure (the measures
asked people how many pills they missed weekly; many people were
prescribed only 1 pill/day, thus there were only 8 options).

Many thanks!