Dear all,

this is my first post.

I am trying to fit a (simple?) multivariate model in `brms`

with two responses coming from different distributions. Both are intercept-only models with the same grouping structure (‘random effects’, see reprex below), so the model I have estimates two intercepts and two group-level variances.

```
bf(resp1 | trials(resp1_trials) ~ 1 + (1|g)) + binomial() +
bf(resp2 ~ 1 + (1|g)) + poisson()
```

Since I know (in the context of simulated data) that the underlying intercept and group level variance is the same for both responses, I would like to constrain the model such that it returns a single (‘shared’) intercept and a single (‘shared’) variance (instead of two each). Is it possible in `brms`

to write the model formula so that it adheres to that constraint (rather than coding the model directly in `Stan`

)?

I know that I could add a fixed (via a constant prior) or estimated correlation term for the group-level intercepts (e.g. here), which gets me closer to what I have in mind, but still estimates two group-level terms.

Any pointer would be highly appreciated.

```
library(brms)
set.seed(123)
g_val <- rnorm(50, mean = 0.3, sd = 1.2)
resp1 <- rbinom(n = 50, size = 100, prob = inv_logit_scaled(g_val))
resp2 <- rpois(n = 50, lambda = exp(g_val))
dat <- data.frame(resp1, resp1_trials = 100, resp2, g = seq_along(g_val))
form1 <- bf(resp1 | trials(resp1_trials) ~ 1 + (1|c|g)) + binomial()
form2 <- bf(resp2 ~ 1 + (1|c|g)) + poisson()
fit <- brm(form1 + form2 + set_rescor(FALSE), data = dat)
fit
par(mfrow = c(1, 2))
p <- ranef(fit)$g[, , "resp1_Intercept"][, "Estimate"]
plot(g_val, p, xlab = "truth", ylab = "estimated for response 1")
p <- ranef(fit)$g[, , "resp2_Intercept"][, "Estimate"]
plot(g_val, p, xlab = "truth", ylab = "estimated for response 2")
```

- Operating System: macOS 12.5
- brms Version: 2.17.0