Multiple membership multilevel models

Abstract: 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.