  Multiple membership multilevel models are an extension of standard multilevel
models for non-hierarchical data that have multiple membership structures.
Traditional multilevel models involve hierarchical data structures whereby
lower-level units such as students are nested within higher-level units such as
schools and where these higher-level units may in turn be nested within further
groupings or clusters such as school districts, regions, and countries. With
hierarchical data structures, there is an exact nesting of each lower-level
unit in one and only one higher-level unit. For example, each student attends
one school, each school is located within one school district, and so on.
However, social reality is more complicated than this, and so social and
behavioural data often do not follow pure or strict hierarchies. Two types of
non-hierarchical data structures which often appear in practice are
cross-classified and multiple membership structures. In this article, we
describe multiple membership data structures and multiple membership models
which can be used to analyse them.
