What is the right mixed effects models for data that is both nested and not? I have a dataset that includes nested observations as well as repeat observations that are not nested (I'm not sure this is the best way to describe it, but stay with me).
Here are the specific details on the data:
I have data on amendments considered on the floor of the House of Representatives. Each amendment is nested (or grouped) by bill, since an amendment can only be offered to one bill. I understand that if this were it for complications with the data I would just run a multi-level model.
HOWEVER, the data are also clustered by the sponsor of each amendment. Amendments are sponsored (or offered) by individual members of Congress. Some members of Congress appear just once having offered just one amendment in the dataset. Other members of Congress appear dozens of times having offered dozens of amendments. The sponsor are not hierarchically nested within each bill as members can and do offer amendments to numerous bills.
My question is what is the most appropriate model, allowing me to deal with the multi-level nature of the data (amendment - bill) and the repeated observations by sponsor? 
I'd know how to deal with each of these independently, but not at the same time. I'm lost. I'll appreciate any help.
 A: This is a cross-classified dataset structure, in that it features (partially) crossed random effects of "bill" and "sponsor." The appropriate model is thus a (generalized) linear mixed model with crossed random effects.
Cross-classified data structures are common in fields like experimental psychology and linguistics -- for example, a common experimental setup involves a sample of participants who all make some response to the same sample of printed word stimuli -- but perhaps not as common in other social science fields, so they have not been as widely studied as hierarchical data structures. But they are commonly applied in certain areas.
Most modern mixed modeling software (but not all) can support models with either crossed or nested random effects. In Stata it looks like the appropriate command would be the xtmelogit command, considering your binary outcome. Unfortunately I can't help you much with the exact syntax.
I have compiled a reading list on introductory mixed models, geared toward cognitive science researchers, which features many papers that focus on crossed rather than nested random effects. I guess you're not a cognitive scientist, but you may still find it useful.
