I have a question related to how to know which prior to use on a given variable. I have no problem fitting models with
rstanarm and I understand the reasoning behind Bayesian analysis but I want to understand better how to choose a specific prior when I have a prior believe. For example, I’m working on an experiment where some schools received money and parental participation in school affairs as a treatment. I want to look at whether this had an effect on test scores. Let’s assume that test scores is a dummy for 0 when
1:7 and 1 when
8:10, where test scores lie between 1 and 10. In the literature, there is mixed evidence on whether this has worked; in some situations it had a positive effect and in others it had little to no effect.
My specific question is which prior to use? I know this is subjective but what is the reasoning behind picking specific families. Sometimes I see binary outcomes (treatment betas) specified with priors such as student t’s or normal priors but that wouldn’t make sense to me because the variable is binary. Should the prior be something like a binomial or geometric distribution? Distributions based on counts rather than continuous variables. I know that this specific treatment is very very unlikely to be negative, very probable to be close to zero allowing for small effects but also leaving small room for a reasonable effect (so a long tail). Of course, all of this applies for a continuous variable but I’m not sure I understand whether I can use these distributions for binary variables.
For my specific treatment beta, I was thinking of a prior distribution on something like a log normal where the bulk of the distribution if slightly above zero but a long tail towards the positive spectrum.
Thanks for any explanations.