What is the 'scale' parameter in 'rstanarm' in general?

Hello,

In this answer, @bgoodri taught me that the scale parameter in `rstanarm::stan_lmer`, to which we assign a Gamma prior with the help of `prior_covariance = decov(......)`, corresponds to the between standard deviation in the case of a one-way ANOVA model with a random factor (`y ~ (1|factor)`).

But what is this parameter for a general Gaussian linear mixed model? For example a two-way ANOVA (with/without interaction). And how to control the prior distribution on the group-levels variance components if there are multiple ones?

I’m lost. Is it something like that:

``````data {
int<lower=1> J; // number of between variances
...
}

parameters {
real<lower=0> tau;
vector<lower=0>[J] theta;
corr_matrix[J] Omega;
...
}

transformed parameters {
real<lower=0> sigma_between_total;
vector<lower=0>[J] sigmas_between;
cov_matrix[J] Sigma;
sigma_between_total = sqrt(J) * tau;
Sigma = quad_form_diag(Omega, sigma_between_total * sqrt(theta));
for(j in 1:J){
sigmas_between[j] = Sigma[j,j];
}
}

model {
tau ~ gamma(shape, scale);
theta ~ dirichlet_rng(rep_vector(concentration, J));
Omega ~ lkj_corr(regularization);
...
}
``````

I don’t think so, because the covariances play no role here…

Tagging @jonah as I don’t understand rstanarm very well…

Best of luck with the model!

Some info here.