ABSTRACT

Most populations studied in the social sciences have a hierarchical structure. In educational research, for example, children’s test scores may be clustered by class and school. Other individual outcomes, such as behavioural and attitudinal measures, may be clustered by household and geographical area. Both of these examples are of a three-level hierarchical structure with individuals at level 1 nested within classes (or households) at level 2 within schools (or areas) at level 3. When individuals form clusters or groups, we might expect that two randomly selected individuals from the same group will tend to be more alike than two individuals selected from different groups. For example, children learn in classes and features of their class, such as characteristics of the teacher and other children in the class, are likely to influence a child’s educational attainment. Because of these class effects, we would expect test scores for children in the same class to be more alike than scores for children from different classes. Hierarchical structures can also arise from having multiple measurements on the same individual, either on different variables at one point in time (multivariate data) or the same variable at several time points (longitudinal or repeated measured data.) In such cases, the multiple measures form the level 1 units and individuals are now at level 2. Measurements taken on the same individual will tend to be more highly correlated than two measurements from different individuals due to the presence of individual characteristics that affect all of his or her outcomes.