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Multilevel Modeling

11. Multiple Spatial Contexts

To appreciate the importance and implications of including this additional spatial level (at level-3), a series of graphical typologies is developed (Subramanian, Duncan et al., 2001). For the purpose of clarity and ease of understanding, we start with the simple case, shown in Figure 8, in which we assume that the differences between places (at both the spatial levels) are the same for both the social class groups. We continue with the use of the term ‘neighborhoods’ to represent level-2 spatial units, and introduce the term ‘regions’ to represent level-3 spatial units.

In Figure 8, the y-axis represents the individual score for poor health, the solid thick line representing the fixed average, the thinner solid lines representing the regions, while the dashed and the dotted lines represent neighborhoods within those regions.

In Figure 8(a) it can be seen that while regions vary significantly around the average line, such that one is high (Region-B) and one is low (Region-A), the neighborhoods within each lie close to their respective region lines. This suggests that there is no need to include neighborhoods as a level, and that a structure of individuals nested within regions is sufficient to capture the main source of geographic variation.

Figure 8a

Figure showing that regions vary significantly around the average line, such that one is high (Region-B) and one is low (Region-A), the neighborhoods within each lie close to their respective region lines as discussed in the text.
In Figure 8(b), the converse is portrayed; while the differences between regions are insignificant (i.e., they are grouped close to the overall average line), those between neighborhoods are substantial. This would suggest the greater importance of neighborhood level compared to region level.

Figure 8b

Figure showing small between region and large between neighborhood-within region variation as described in the text.
Finally, Figure 8(c) anticipates a situation with significant variation at both region and neighborhood levels. While the relative importance of each might vary, both levels need to be included in an empirical model.

Figure 8c

Figure showing significant between region and between neighborhood within region as described in text.
Subramanian, S. V., Duncan, C., et al. (2001) Multilevel perspectives on modeling census data. Environment and Planning A 33(3): 399-417.