I am wondering how best to code using the same linear predictor in multiple responses, in BRMS. As a simple example, imagine we are counting alive birds and dead birds 🐦. The mean total number of birds depends on some covariates:

\mu = \sum_i \beta_i x_i

The number of alive birds is:

b_a \sim \mathrm{Poisson}(p_a \mu)

The number of dead birds is:

b_d \sim \mathrm{Poisson}((1-p_a) \mu)

I have read about coding multiple responses in BRMS but am looking for an example of sharing the same linear predictor between the multiple responses in this way. Any pointers welcome 🙂