Hi,

I am fairly new to Bayesian and have a question about how to specify the priors for the hyper parameters in a hierarchical varying intercept model. In other words, I would like to know the default assumptions on the hyper priors for the mean of the overall intercept and its sigma, and if those defaults can be changed. Here is the model specification

Mglm1 <- stan_glmer(gal_log ~ 1 + FishSumEdible1000 + LargeGameSumEdible1000 + atvs + sms + boats + cars + (1 | commname), data = modelData, family = gaussian(link = “identity”), prior = normal(location=0,scale=100,autoscale=F),prior_intercept = normal(location=0,scale=1000,autoscale=F), prior_aux = exponential(rate=1))

Thanks for clarifying.

There isn’t a hyperprior on the inputs to the `prior_intercept`

function. Although there are a few families to choose from, all of the inputs are known values. So, when you do `prior_intercept = normal(location = 0, scale = 1000, autoscale = FALSE)`

then that is just a \mathcal{N}\left(0, 1000\right) prior. Also, 1000 is too big for the standard deviation, particularly when the outcome variable is in log units.

Are you suggesting to pick a different family in order to turn it into a fully hierarchical model?

No, and there is no such option in **rstanarm**. There is just a fixed prior on the overall intercept and normal priors (with mean zero) on the deviations from the overall intercept when you include a `+ (1 | commname)`

in the formula for `stan_glmer`

.

Thanks very much! That’s very helpful.