Is there a generic weakly informative prior that doesn't require rescaling?

Question

This seems to be the go-to recommendation when considering a prior for a model.

In my case, I am running mixed effects (with random subject and item effects) regressions (both linear and logistic), and am looking for a single weakly informative prior to put on all fixed effects and their interactions.

The prior that seems to be suggested in the resource I linked to is a Cauchy distribution with a mean of 0 and a scale of 2.5. However it assumes that: all binary predictors are centred at 0 and have a difference of 1 between low and high values. It also assumes that all continuous predictors have a mean of 0 and a sd of 0.5

I am hesitant to rescale all of my variables. Is there a well regarded generic weakly informative prior that doesn't require rescaling?

Answer 1

Rescaling all variables in a linear or generalised linear model is like removing a number of degrees of uncertainty by having all coefficients brought to the same scale. In weakly informative situations, this reduces both the variability of the estimates and the impact of the prior choices.

The prior that seems to be suggested in the resource I linked to is a Cauchy distribution with a mean of 0 and a scale of 2.5.

This is but one choice of prior for the model to be analysed. As advocated on the Stan wiki at the other end of the link. Just like every other prior, it impacts the value of the estimates and of the tests conducted on these estimates and should be used in a relative sense, i.e., by measuring the difference between prior and posterior brought by the data. (I will not repeat here my longer X validated post about non-informative priors.)