I'm trying to capture the following scenario with a multilevel logistic regression: The presence of a trait [0,1] was assessed in participants at 5 sites in Northern and Southern California, south-ca [0,1] (additional subject-level predictors will be added later on).
M1 <- stan_glmer(trait ~ south-ca + (1|site),
data = dat,
family = binomial(link = "logit"),
prior = normal(),
prior_intercept = normal())
Since I have only 5 groups/sites in the model and I know that the between-groups variance is small, I am particularly concerned about the prior for the group-level variance parameter (cf. Gelman & Hill, 2007, chapter 19.6). I'd like to follow Gelman and Hill's example of using a half-Cauchy prior distribution but I'm uncertain about the syntax which presumably involves the "prior_aux" option. Can anyone help? Thanks!