Multivariate distributional models, conditioning multiple parameters on the predictors

Interfaces brms
1

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

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

2

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

3

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.

4

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)
)