I appreciate it if someone helps me to define the following multilevel model with hierarchical (adaptive) priors in brms.

The model is a binary logistic regression where intercept and coefficients are grouped by the “grp” variable:

```
y ~ Bernoulli(p)
logit(p) = intercept[grp] + b_1[grp] * x_1 + b_2[grp] * x_2
intercept ~ Normal(mu_0, sigma_0)
mu_0 ~ Normal(0, 1)
sigma_0 ~ HalfCauchy(0, 1)
b_1 ~ Normal(mu_1, sigma_1)
mu_1 ~ Normal(0, 1)
sigma_1 ~ HalfCauchy(0, 1)
b_2 ~ Normal(mu_1, sigma_1)
mu_2 ~ Normal(0, 1)
sigma_2 ~ HalfCauchy(0, 1)
```

**brms code I have so far:**

```
brm(formula = y | trials(1) ~ 1 + (1 | grp) + (0 + x_1 | grp) + (0 + x_2 | grp)
family = binomial,
prior = c(prior(normal(0, 1), class = Intercept),
prior(cauchy(0, 1), class = sd)),
data = dat,
iter = 5000, warmup = 1000, chains = 4, cores = 4, control = list(adapt_delta = 0.98))
```

*Note: I intentionally used binomial family instead of bernoulli, but don’t remember the reason!*

**1. Is the brms code defines the model?**

**2. How do I specify the priors for mu_1 and mu_2?**

**3. I guess I should include population-level effects too. Can missing these effects in the model be the reason for the long running time? (i.e., 1 hour, 180 samples, 100 variables, grp variable has 11 distinct values)**

Thank you,

- Operating System: Windows 10
- brms Version: 2.7.0