Ecological Correlation and Centering Around Group Means in 2-Level Model

An ecological correlation is a correlation based on group averages. Ecological correlations as such can be misleading, because the variability in the underlying individual data is lost by using averages. In interpretation of the results, there is a danger of committing the ecological fallacy: data is analysed at one level and inferences are made to another level (Robinson 1950). In 2-level model, the effect of the variable can be divided in group effect and individual effect within the group. This is done by centering the individual level explanatory variable around the group means and using the centered individual level variable jointly with the group level averages as explanatory variables. The ecological correlation affects only the estimate of the group effect, and the individual level effect is estimated using individual level correlations within the groups.