Newbie question: does ‘unit-scale’ imply that one should work with standardized variables when using weakly informative priors? Saw the term mentioned several times while reading about weakly informative priors. I work with psychological variables.
When fitting models in brms, it’s generally a good idea to use standardized variables, when applicable, regardless of the kinds of priors you’re working with. But without a quote or a hyperlink, it’s hard to speak directly to the material you’ve been reading on weakly informative priors.
I am referring to material such as this:
I understand it’s not only relevant to weakly informative priors. Am I correct that the main benefit is for interpretation purposes in general, and more specifically, to understand where most of the probability mass is located for such a prior, given the type of effects one is expecting. For example, if you expect effects around 0.1 or 0.2, then even a normal(0, 1) prior places most of the probability mass elsewhere?
PS: thanks for your brms version of McElreath’s book. I found it extremely helpful.
Interpretability is part of the reason—both substantively and when choosing priors. But it’s also the case that HMC often works more efficiently with standardized variables. You might get faster sampling, higher effective samples, and lower autocorrelation when using standardized variables. Relatedly, standardizing might also help you avoid nasty difficulties like divergent transitions.
W/r/t to the Prior Choice Recommendations wiki, I’d take the first paragraph as clarifying your question:
The above numbers assume that parameters are roughly on unit scale, as is done in education (where 0 is average test score in some standard population (e.g., all students at a certain grade level) and 1 is sd of test scores in that population) or medicine (where 0 is zero dose and 1 is a standard dose such as 10mcg/day of cyanocobalamin, 1,000 IU/day cholecalciferol, etc.; these examples come from Sander Greenland). (emphasis added)
PS to your PS: Oh great! I’m glad it’s helpful.