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Multilevel Modeling

8. A Graphical Introduction

Figure 6(a) presents the simplest outcome: differences between social groups but no variation between neighborhoods. With only one fixed average for each group, it shows an individual-level model in which the same relationship is fitted to all neighborhoods.

Figure 6a

Figure presenting differences between social groups but no variation between neighborhoods as described in text.

Figure 6(b) represents a two-level model with each of six neighborhoods having its own poor health/social class relationship. The thick solid lines represent the average poor health rates for the two groups, while the symbol-lines (one for each neighborhood) represent the variation between neighborhoods around the average line. Since the individual relationship between social class and poor health is also shown in the model, the graph implies that the variation between neighborhoods is not due solely to the varying social composition of neighborhoods and is, therefore, contextual. The neighborhood differences, however, are assumed to be simple such that neighborhoods that are high for one group are also high for the other and vice versa (similar to the ‘random-intercepts’ model). Thus, while there is a (contextual) geography of poor health, it can be summarized in one map.

Figure 6b

Figure representing a two-level model with each of six neighborhoods having its own poor health/social class relationship as described in text.

We can, however, anticipate the neighborhood variation to be significantly different for the two groups. This difference consists of two dimensions. First, the amount (range) of neighborhood variation can be different for the two groups. In Figure 6(c), those in the high social class category tend on average to have lower chances of being in poor health, but the neighborhood variation is relatively large as compared to the low social class. For the low social class, it is the reverse: a higher probability of being in poor health, on average, but smaller variation between neighborhoods.

Figure 6c

Figure illustrating that the second aspect of the neighborhood difference relates to the ordering. Thus, neighborhoods that are high for one group may be low for the other and vice versa as described in text.

The second aspect of the neighborhood difference relates to the ordering. Thus, neighborhoods that are high for one group may be low for the other and vice versa, as shown in Figure 6(c). An attractive feature of multilevel models – one that is commonly used in health research – is their ability to model contextual differences as a function of characteristics that relate to neighborhoods, in addition to individual characteristics. At the same time, the nature and type of interactions between individual characteristics and neighborhood characteristics can also be assessed.