# Multivariate distributional models, conditioning multiple parameters on the predictors

I am building a multivariate zero/one inflated beta regression model:

formula <- bf(
A ~ x1x2 + (1+x1|p|participant),
B ~ x1
x2 + (1+x1|p|participant))

This conditions the betas on the predictor. What if I also want to condition the zero inflation parameter (i.e. zoi~ x1*x2 + (1+x1|p|participant)) on the predictors (for theoretical reasons)? Each of the two outcomes is expected to have a different zoi, but I’m not sure as to how to specify them.

can you show the full formula (i.e. bf call) of your model?

Sure. This would be the two models I want to run as multivariate [not sure yet with the random effects in the zoi parameter, still trying it out on simulations]:

m1 <- brm(
bf(
lexical_tok1 ~ 1 + ASD * Visit + (1 + Visit | p | ChildID),
zoi~1 + Visit * ASD + (1 + Visit | p | ChildID)),
data=d,family=zero_one_inflated_beta(),chains=2,cores=2)

m2 <- brm(
bf(
syntax_penn_tok2 ~ 1 + ASD * Visit + (1 + Visit | p | ChildID),
zoi ~ 1 + Visit * ASD + (1 + Visit | p | ChildID)),
data=d,family=zero_one_inflated_beta(),chains=2,cores=2)

What I would want basically is to model a correlation between the random effects across the two models (as the phenomena and the zero inflations are theoretically connected). However, I am not sure as to how to specify two different “zoi” parameters in the same multivariate model. And yes, theoretically, I’d expect two different (but correlated) zoi for the two phenomena.

The formula argument should be

bf(
lexical_tok1 ~ 1 + ASD * Visit + (1 + Visit | p | ChildID),
zoi~1 + Visit * ASD + (1 + Visit | p | ChildID)
) +
bf(
syntax_penn_tok2 ~ 1 + ASD * Visit + (1 + Visit | p | ChildID),
zoi ~ 1 + Visit * ASD + (1 + Visit | p | ChildID)
)