Chapter 6 Other uses of Multiple Membership Models
Multiple membership models can be combined with a number of other model types, and they are not restricted to only one level. It is possible to have multiple membership at level 2, but a pure hierarchy at level 3. Multiple membership models can be combined with a three level model to incorporate longitudinal data as well (for example Leroux 2019). They can also be combined with cross-classified models Beretvas (2011) to handle even more complex data structures.
A use I found particularly interesting for multiple membership models was to handle missing data. Hill and Goldstein (1998) proposed using a multiple membership structure to equally weight all possible schools for a student when actual school enrollment was unknown. For students who had a known school membership, they were simply members of one school, with a weight of 1. I found this an interesting approach to missing data, as you are still able to use the student information, though with less school information than those students who have a known membership.