Multilevel Modeling

6. Multilevel Data Structures

Besides extending the two-level structure to a three-level structure of, for example, individuals (level-1) within neighborhoods (level-2) within counties (level-3), a number of other data structures can be thought to be special cases of multilevel models. For instance, health outcomes and behaviors as well as their causal mechanisms are rarely stable and invariant over time, producing data structures that involve repeated measures.

Two possibilities arise depending on the unit that is repeatedly measured. When individuals are repeatedly measured within a panel design, the outcomes taken at different times form level-1. The same outcomes measured over different times are nested within individuals at level-2, which in turn nest within higher-level units (e.g., neighborhoods). This structure is shown in Figure 3(a) and allows the assessment of individual change within a contextual setting. The other possibility is a repeated cross-sectional survey, where places are monitored at regular time intervals (repeatedly measuring places over time).

Figure 3a

Figure of panel design as described in text.

The structure would then be: individuals at level-1, time/years within places at level-2, and places at level-3, as shown in Figure 3(b). Such a structure permits an investigation of trends within geographic settings controlling for their compositional make-up. Multilevel models could be used to explore what sorts of individuals and what sorts of places have changed with respect to health outcomes.

Figure 3b

 Figure of repeated cross sectional design as described in text.

When different responses/outcomes are correlated this lends itself to a multivariate multilevel data structure in which level-1 are sets of response variables measured on individuals at level-2, nested in neighborhoods at level-3. The key feature is that the set of responses (outcomes) is nested within individuals. The response could be a set of outcomes that relate to, for instance, different aspects of health behavior (e.g., smoking and drinking). Crucially, such responses could be a mixture of ‘quality’ (do you smoke/do you drink) and ‘quantity’ (how many/how much). A multilevel structure on different aspects of health behavior could include measurements (e.g., smoking and drinking, both at level-1), nested within individuals (at level-2), within neighborhoods (at level-3).

The substantive benefit of this approach is that it is possible to assess whether different types of behavior are related to individual characteristics in the same or different ways. Moreover, the residual co-variances at level-2 and level-3 measure the ‘correlation’ of behaviors between individuals and between places. Additionally, we can ascertain whether neighborhoods that are high for one behavior are also high for another; and whether neighborhoods with high prevalence of smoking, for instance, are also high in terms of the number of cigarettes smoked.

Technical benefits flow in terms of efficiency if the response is correlated and if there are many missing responses, as in matrix sample designs. Figure 3(c) presents a structure where the responses at level-1 capture different aspects of health behaviors and Figure 3(d) portrays the idea of ‘mixed’ (quality and quantity) responses on a particular aspect of health behavior.

Figure 3c

Figure of multivariate responses as described in text.

Figure 3d

Figure of mixed multivariate responses as discussed in text.