 # Multivariate brm models

• Operating System: Windows 10
• brms Version: 2.4.3

Hi All,

I’m trying to understand what exactly brms is doing with the following model:

bf_1 <- bf(y|trials(n)~z+x)+binomial()
bf_2 <- bf(x~z)+gaussian()

brms.out <- brm(bf_1+bf_2+set_rescor(FALSE),data=dat,
chains = 2, iter = 1000,
warmup = 500, thin = 1,

I’d really like to be able to write down this model in mathematical notation. But I can’t figure out from the output how this model is any different than the following:

brms.out2 <- brm(bf_1,data=dat,
chains = 2, iter = 1000,
warmup = 500, thin = 1,
brms.out3 <- brm(bf_2,data=dat,
chains = 2, iter = 1000,
warmup = 500, thin = 1,

Any guidance?

In the current specification the multivariate model is equivalent to the two univarite ones. This is because there is nothing that relates your two univariate models to each other. Currently, there are two ways to achieve this in brms.

First, you can model residual correlations but that’s only possible for certain family combinations such as multivariate gaussian model (and not for gaussian-binomial).

Second, you can model the varying effects of the models as correlated, but that of course only applies if you have multilevel structure in your data.

For more details see https://cran.r-project.org/web/packages/brms/vignettes/brms_multivariate.html

you can model residual correlations

Does this change the estimation of effects compared to the univariate models, or does it just provide more information about the unmodeled parts of the dependent variables? Should the modelled effects depend on `set_rescor`?

Modeling rescor might change estimates of the other parameters. For an example in the context of causal inference, you make take a look at this blog post: https://rpsychologist.com/adherence-analysis-IV-brms