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Multilevel Modeling

8. A Graphical Introduction

We illustrate the idea of such cross-level interactions by building on our running example of a two-level model (individuals at level-1 within neighborhoods at level-2) with the response being a score for poor health for each individual. We consider the categorical individual predictor, social class (with high social class as a reference and low social class specified as a contrast indicator variable), and a continuous neighborhood-level contextual predictor (e.g., socioeconomic deprivation index). Figure 7 portrays a range of hypothetical graphical models. In Figures 7(a)-(h), y-axis represents the poor health score and the x-axis shows the neighborhood socioeconomic deprivation index. The dashed-line represents low social class, and the solid-line represents high social class.

Figure 7(a) shows marked differences between high social class and low social class but no contextual effect for neighborhood socioeconomic deprivation (all individual, no contextual). Figure 7(b) represents the converse: small difference between the two social groups but a large contextual effect of socioeconomic deprivation (all contextual, no individual). The parallel lines in Figure 7(c) and 7(d) show both individual and contextual effects. In Figure 7(c), the neighborhood socioeconomic deprivation is shown to have a detrimental effect on the health of the individuals and the reverse is shown in Figure 7(d).

The key point is that the contextual effect of socioeconomic deprivation is seen to be the same for both high social class and low social class. Put differently, while neighborhood socioeconomic deprivation explains the prevalence of poor health, it does not account for the inequalities in health between the social class groups. In Figure 7(e) contextual effects are different for different groups. They are shown as positive for high social class and negative for low social class, such that in neighborhoods with highest level of socioeconomic deprivation health inequalities are minimum.

Thus, neighborhood-level socioeconomic deprivation is not only related to average health achievements but also shapes social inequalities in health. Figure 7(f) represents the case where contextual effects are strong enough to invert the individual effects. Figures 7(g) and 7(h) show models in which non-linear terms are of importance, such that the smallest or largest group inequalities in health are found respectively at ‘average’ levels of socioeconomic deprivation and not at the extreme levels of neighborhood socioeconomic deprivation.
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Figure 7

Figure 7 portrays a range of hypothetical graphical models. In Figures 7(a)-(h), y-axis represents the poor health score and the x-axis shows the neighborhood socioeconomic deprivation index. The dashed-line represents low social class, and the solid-line represents high social class as described in text.