I would like to fit a multivariate causal model in `brms`

, according to the following hypothesized DAG:

Through the model, I want to understand the total effect of the treatment `a`

on both outcomes `y1`

and `y2`

, while taking into account a mediator `m`

and another covariate `b`

. I further want to understand the correlation between the outcomes `y1`

and `y2`

.

This was my attempt so far:

```
model <- brm(
data = data,
bf(y1 ~ 1 + a + b + m) +
bf(y2 ~ 1 + a + b + m) +
bf(m ~ 1 + a) +
set_rescor(TRUE)
)
```

This estimates the residual correlation between y1 and y2, but also between y1 and m and y2 and me, which I am not interested in. Is it possible to exclude those correlations somehow from the covariance matrix?

I am not an expert in causal modelling, so my problem may be ill-posed. Any thoughts on how to approach this problem are greatly appreciated.

- Operating System: Windows 10
- brms Version: 2.17.0