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.

Figure 3e

Figure of cross classified structure as described in text.

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.

Figure 4

Multilevel Structure of Repeated Measurements of Individuals over Time Across Neighborhoods with Individuals Having Multiple Memberships to Different Neighborhoods Across the Time Span

Figure of multilevel structure of repeated measurements of individuals over time as described in text.
Source: Subramanian 2004 Subramanian SV. The relevance of multilevel statistical models for identifying causal neighborhood effects. Social Science and Medicine. 2004;58:1961-1967.

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.

Example 2

Individual 25 moved from neighborhood 1 to neighborhood 25 during the study time-period t1-t2, spending 20% of her time in neighborhood 1 and 80% in her new neighborhood. This multiple-membership panel design could allow control of changing context as well as changing composition, besides enabling a consideration of weighted effects of proximate contexts (Langford, Bentham et al., 1998). So, for example, the geographical distribution of disease can be seen not only as a matter of composition and the immediate context in which an outcome occurs, but also as a consequence of the impact of nearby contexts, with nearer areas being more influential than more distant ones. Goldstein, (2003) provides an elegant and comprehensive classification schema.

Jones, K., Gould, M. I., et al. (1998) Multiple contexts as cross-classified models: The labor vote in the British general elections of 1992. Geographical Analysis 30: 65-93.
Goldstein, H. (2003) Multilevel statistical models. London: Edward Arnold.
Goldstein, H. (1994) Multilevel cross-classified models. Sociological methods and research 22: 364-375.