Hi Everyone,

The documentation of brms “prior” function says something about the intercept that sounds important, but I need help in understanding that.

"*the intercept has its own parameter class named "Intercept" and priors can thus be specified via set_prior("<prior>", class = "Intercept")… Note that technically, this prior is set on an intercept that results when internally centering all population-level predictors around zero to improve sampling efficiency. On this centered intercept, specifying a prior is actually much easier and intuitive than on the original intercept, since the former represents the expected response value when all predictors are at their means. To treat the intercept as an ordinary population-level effect and avoid the centering parameterization, use 0 + Intercept on the right-hand side of the model formula.*

" (link)

If for example I want to run a basic regression y ~ x1 * x2 + ( x1 * x2 | group ) where x1 and x2 are dummy coded factors that are not centered (0/1). Should I give the intercept a prior that will reflect my belief regarding the grand mean, or should I give the intercept a prior that reflect my belief regarding y values when x1 and x2 are zero? I always thought the latter is the correct way, but reading the above documentation I am now not sure…

Thank you,

Nitzan