Hierarchical Linear Modeling

Hierarchies

Hierarchical structures involve lower level units nesting within higher level units. Throughout this entry, the lowest level of observation in the hierarchy is referred to as Level 1, where units are nested within groups and these groups are referred to as Level 2; and when these groups are nested within higher order groups, the higher order groups are referred to as Level 3. Figure 1 demonstrates two hierarchies: a two-level hierarchy (a) with students (Level 1) nested within schools (Level 2) and a three-level hierarchy (b) with students (Level 1) nested within classrooms (Level 2) and within schools (Level 3).

Figure 1 Pictorial representation of (a) two-level hierarchy and (b) three-level hierarchy

Many kinds of data in the social sciences have a hierarchical structure, and it is worth noting that individuals are not always the Level 1 units. If schools were the unit of analysis, then schools (Level 1) could be nested within local authorities (Level 2). Equally, measurements taken at multiple time points (Level 1) may be nested within the individuals who were measured (Level 2). Research design can create data hierarchies through sampling. Clustered sampling techniques, or cluster randomized control trials, specifically recruit groups of people within hierarchies. Higher level units, such as schools, are selected for participation rather than randomly selecting individual students (Level 1).

Once hierarchies are established in the social world, they result in nonindependent (correlated) data. This can be the result of selection (where the characteristics of the individuals determine their groupings) and social processes (the interaction between individuals within groups, and exposure to the same context). For example, in some cases, schools attract students with similar characteristics (e.g., socioeconomic position, exam performance, and ethnicity) partially because of the schools’ location and performance. Therefore, selection into schools results in students having similar characteristics and behavioral patterns than would be expected if selection into schools was random. In addition, socialization processes and interactions with other students and staff in the same school cause students to become more similar through the formation of perceived or actual social norms about expectations and behaviors. Therefore, even if allocation to higher level groups (in this example schools) was random at the outset, social processes and the exposure to the same environment create similarities in the group members. This creates dependence in the data when measuring the group members, which can be accounted for by using hierarchical linear models.

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