# Brms: multivariate response, different distributions

I am interested in modelling survival (0/1) and reproduction (# offspring 0…3) as a multivariate response, combining Bernoulli with (truncated) Poisson distributions. Is it possible to do this with brms?

A model could look a follows:

``````bform <- bf(survival ~ ..., family = bernoulli()) +
bf(offspring | trunc(<value>) ~ ..., family = poisson())

fit <- brm(bform, ...)
``````

However, without correlated multilevel structure on the right-hand side of the model formulas, this model will just be equivalent to two univariate ones.

Thanks Paul. Is it possible to add a correlated multilevel structure on the rhs? Specifically, I want to model correlated year-effects to both survival and offspring. So, if I would add +(1|p|year) to both formulas, would a bivariate normal be estimated?

Exactly.

Great, thanks! Is it also possible to model the correlated year-effects as multivariate t-distributed or multivariate skew-normal rather than “ordinary” multivariate normal?

Student-t is possible albeit not documented and not yet officially supported until we better understand its implications. Go for `(1 |p| gr(year, dist = "student"))`.

Thanks again. I will give the multivariate t a try because I have the impression that the year-effect empirical distribution has “fat tails”.

One more thing: when using the predict function, is it possible to marginalize/integrate over the “random” year effects, in order to obtain expected survival and offspring number?

BTW: thanks for creating bmrs. It looks like an enormously useful package that will save me a lot of Stan coding.

You can ignore random effects via `re_formula = NA` but marginalizing is a much more difficult thing (read: not yet possible).

I have used the make_stancode call to generate two Stan files (below). One is with a Gaussian distribution for the random effects, and the second is using the gr() function to obtain Student-t distributed varying effects (as noted above by Paul). I have added the model specification at the top of the files for reference.

Could someone highlight where exactly in the Stan code the t-distribution is being specified on the random effects? I see a definition of a df variable and the priors for this variable, but it is not clear where exactly the change is specified.

Thank you!

ND_distrib.stan (3.1 KB) t_distrib.stan (3.2 KB)