# Multilevel Modeling

## 12. Multilevel Residual Mapping

While it is the variances that are estimated in a multilevel model at each of the specified levels, it is possible to estimate place-specific (posterior) residuals at each of the contextual levels. Residual mapping is an extremely useful application of multilevel models, especially when the interest lies in simultaneous multiple geographies, and when all the units at each of the geographic level can be observed in the analysis (e.g., the census) (Subramanian, Duncan et al., 2001). In order to appreciate this, Figure 9 unpacks the way in which residuals are constructed when there are two spatial levels.The region-specific residuals (υ_{0k}) at level-3 represent the difference from the fixed average line,* β _{0}*. For example, REGION-A will have a negative residual given its lower rate of poor health compared to the overall average. REGION-B, in contrast, will have a positive residual, given its high rate compared to the average. Neighborhood-specific residuals (u

_{0jk}) at level-2, meanwhile, are measured as the difference from their respective regions to which they belong (hence, the subscript jk) and

*not*as a difference from the fixed average.