# Brms: multivariate response, different distributions

#1

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?

#2

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.

#3

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?

#4

Exactly.

#5

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?

#6

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"))`.

#7

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.

#8

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