Adding a known amount of random error to a model

Questions
2

To try to address these sorts of models, the best way in my opinion is to write down the math of the generative process. You have:

  1. The base probability (and its logodds) logit(p_{base})
  2. The error \varepsilon.
  3. The prem.

Your generative process will look like this:

\varepsilon \sim Normal(0, 0.2)\\ prem \sim Uniform(-2, 2)\\ Outcome \sim Bernoulli(expit(\varepsilon + prem + logit(p_{base})))

However, you have to be aware that it will be hard if not impossible to distinguish between the effects of \varepsilon and prem (the parameters might be unidentifiable)