I have a discrete variable with a scale from 0 (no issue) - 3 (severe issue). Because what constitutes an issue, is really a quite relative concept (especially when comparing different regions), I am considering demeaning this variable by group. This has two advantages:
  1. I would argue that is has a better interpretation, because the variable now signals the difference from the mean by group, which I would argue to be much more informative.
  2. The variable is no longer ordinal, but continuous (which in my case is a big advantage because I want to instrument this variable icw a control function).
Are there any downsides to this approach, or am I overlooking something important?
I would be very grateful for an authoritative source on this subject.