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RDD: think about centering of running variable and priors
People often centre the running variable, such that the threshold is at zero. This will change the parameters which is very relevant for the Bayesian model because of the priors. The advantages of centering the running variable are that:
- the parameters are easier to interpret
- the coefficient for the main effect of treatment is always(?) equal to the discontinuity at threshold.
While we might not escape the need for custom priors (when the time comes; for example on the intercept parameter), centering the running variable might make things easier. So need to think about doing this automatically, or simply making the user aware of the issues. If we do, then the treatment_threshold
kwarg should be removed and hard-wired to zero.
My initial feeling is to not enforce centering, rely upon the users understanding, and provide the information in the docs and examples.