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Multilevel Modeling

8. A Graphical Introduction

One of the main attractions of multilevel models for public health research is their ability to allow relationships to vary across different contextual settings.

We illustrate this with a two-level structure consisting of individuals at level-1 nested within neighborhoods at level-2 with a single continuous outcome (e.g., poor health score) and a single continuous individual (compositional) predictor (e.g., age) centered about its mean.

Figure 5 illustrates a range of hypothetical graphical models for representing this data structure. In Figure 5(a), the poor health/age relationship is shown as a straight line with a positive slope: older people generally have poorer health. This model conceptualizes health status only in terms of an individual’s age, and the neighborhood context is ignored.
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Figure 5a

Graph of fix intercept, fixed slope

This is remedied in Figure 5(b), in which the relationships in each of the neighborhoods (six here, but typically more) is represented by a separate line at a varying distance from the general underlying relationship, as shown by the thicker line. The parallel lines imply that while the poor health/age relationship in each neighborhood is the same, some neighborhoods have uniformly higher levels of poor health than others.

Figure 5b

Graph of random intercepts, fixed slope

Figure 5c-f

Figure of four graphs with random intercepts, random slopes with positive, negative and no relationship as discussed in text.