Hi, I’m trying to set up a two level Poisson regression in which the second level coefficients should have a normal mixture prior in order to be able to create clusters based on the second level grouping.

More specifically, I have frequencies of use of different websites from several days from several people, and in the first level I’m adding some day level variables (like for example the week and if they had an exam that same day), and i have individual level information in the second level. I want to cluster the individuals, so I want to make a mixture on the coefficients of that level. I’m new with brms, and I can’t seem to find how to include the mixture of normal as a prior, and not as a family. For now I thought about setting the Family to be a poisson mixture, and add normal priors at the second level. Something like this:

```
ml_formula <- bf(y ~ 1 + b1 + b2*week + b3*exer + b4*teach + b5*exam + b6*p1_w b7*p2_w + b8 * p3_w + b9 * p4_w,
mvbind(b1, b2, b3, b4, b5) ~ (1+ p1+p2+p3+p4+demografic1|w|mm(student,website)),
)
ml_prior <- c(prior(normal(0,2), resp="b1", coef = "b1", dpar = "mu1"),
prior(normal(0,2), resp="b1", coef = "b1", dpar = "mu2"),
prior(normal(0,2), resp="b2", coef = "b1", dpar = "mu1"),
prior(normal(0,2), resp="b2", coef = "b1", dpar = "mu2"),
prior(normal(0,2), resp="b3", coef = "b1", dpar = "mu1"),
prior(normal(0,2), resp="b3", coef = "b1", dpar = "mu2"),
prior(normal(0,2), resp="b4", coef = "b1", dpar = "mu1"),
prior(normal(0,2), resp="b4", coef = "b1", dpar = "mu2"),
prior(normal(0,2), resp="b5", coef = "b1", dpar = "mu1"),
prior(normal(0,2), resp="b5", coef = "b1", dpar = "mu2"),
mix <- mixture(poisson,poisson)
fit1 <- brom(formula= ml_formula, data = data, family = mix, prior = ml_prior)
```

Am I doing the right thing? Thanks in advance for the help!