Is there a reasonable way to report a summary measure in the presence of effect modification?


I have an effect that varies based on income (measured in quintiles in the population + the sample does not have an even distribution in the quintiles). The effect is strong in the lower income quintiles and basically non-existent in the highest income quintile. I’m being told to provide a single effect estimate - which “should be easy” by just “controlling for income”. Am I being stubborn by saying we shouldn’t do this? Is there a good way to do this? If I’m right, is there a good source that outlines the reasons not to do this?


Quintiles are not a good way to think of income, because it uses cutpoints (often a bad idea in and of themselves) that are divorced from subject matter meaning. But assuming that interaction is present on the more appropriate continuous income scale also, then you can present two things:

  1. “Chunk” test for the combined main effect and interaction test. This tests whether there is an effect of the other variable, for any level of income.
  2. Plot the effect of the other variable as a function of levels of income. If income were really discrete this could be 5 curves, one for each income interval. If continuous, then a color image plot not unlike a heatmap works well, or a contour or wireframe 3-d plot.