Multilevel Modeling

6. Multilevel Data Structures

Crossed Structures

All the previous examples are strictly hierarchical in that all level-1 units can belong to one and only one level-2 unit. However, data structures can be ‘non-hierarchical.’ Individuals live their lives in a number of overlapping settings such as neighborhoods, work place, home, etc. Such contexts do not always lend themselves to a neat hierarchical structure. Instead, the different settings may overlap at the same level, thus producing a crossed structure. While the importance of such structures has long been recognized, it is only recently that it has become technically and computationally tractable (Goldstein, 1994; Jones, Gould et al., 1998). The ‘quasi-hierarchical’ format employed within cross-classified multilevel models enables an assessment of the relative importance of a number of different, overlapping contexts after allowing for the differential composition of each. As such models identify contexts that have a confounding influence, they also ascertain which contexts have the greatest significance.

For example, a cross-classified model of health behavior (e.g., smoking) could be formulated with individuals at level-1 and both residential neighborhoods and workplaces at level-2, as shown in Figure 3(e). If account is not taken of this cross-classified structure, what may appear to be between-work place variation could actually be between-neighborhood variation and vice versa.

A related structure occurs where for a single level-2 classification (e.g., neighborhoods), level-1 units (e.g., individuals) may belong to more than one level-2 unit and these are also referred to as multiple membership designs. The individual can be considered to belong simultaneously to several neighborhoods with the contributions of each neighborhood being weighted in relation to its distance (if the interest is spatial) from the individual.

While for the purpose of clarity and ease of understanding we have discussed each of the multilevel structures separately, readers are urged to think about these structures in an integrated manner. For instance, a structure can be a combination of more than one of the designs discussed above, as shown in Figure 4.

Time measurements (level-1) are nested within individuals (level-2) who are in turn nested in neighborhoods (level-3). Importantly, individuals are assigned different weights for the time spent in each neighborhood.