# Prior distribution for group-level mean

Dear Stan experts,

Hyper priors for group-level mean and standard deviation have to be specified in hierarchical model. I found a lot of discussion about different prior for SD( Like the discrepancy between Half-Normal, Half Cauchy) in stan forum, however, i did not find too many discussions about the group-level mean prior. I wonder does the choice of prior for group-level mean has a large impact on the estimation result? For instance, if i want to estimate a regression coefficient, uniform flat prior, laplace prior or gaussian prior which one is best for for group-level mean parameter? Thanks in advance.

Best,

Hi, @mingqian.guo: Sorry this took so long for such a relatively simple question.

A standard strategy is to set all of the random effects prior means to zero. That just pulls the effects out into the global intercept, which usually has a wider prior due to soaking up effects from elsewhere. That is, rather than y_n \sim \textrm{normal}(\alpha + \beta_{\textrm{sex[n]}}, \sigma) with \beta \sim \textrm{normal}(\mu, \tau), take y_n \sim \textrm{normal}(\alpha + \mu + \beta_{\textrm{sex}[n]}) with \beta \sim \textrm{normal}(0, \tau). Then it’s clear you should just eliminate \mu and absorb its value into \alpha (this is why intercepts often get wider priors).

For random slopes, you want to think about what the range of possible slope values are. And you still probably want to use a non-centered parameterization to the extent possible.