ZOIB model brms random effects structure

Modeling
1

Hi all,
I had a quick question about the model formula when fitting a multilevel ZOIB model, particularly about the random effects. I have a data set with rating data between (and including) 0 and 1 (continuous scale using a visual analog scale (VAS)), predicted by the interaction of two within-subject variables. With regard to the random effects, I’m not entirely sure if it is advisable to fit the same random effects structure for each ZOIB model parameter, namely if the random slope is necessary for each parameter. Does anyone have suggestions/experiences with such models?

formula = bf(
  rating ~ occupation*variety + (occupation*variety | id), 
  phi ~ 1 + (1 | id), 
  zoi ~ 1 + (1 | id), 
  coi ~ 1 + (1 | id)
)

or

formula = bf(
  rating ~ occupation*variety + (occupation*variety | id), 
  phi ~ 1 + (occupation*variety | id), 
  zoi ~ 1 + (occupation*variety | id), 
  coi ~ 1 + (occupation*variety | id)
)

Many thanks, and let me know if I should provide any more details!

2

Assuming there is 1 process for all of the outcome components, you should use the same model formula across the specifications, though you can leave out phi. That is an ancillary parameter.

But I will say, if you do have a single scale, then you should also check out my ordbetareg package, which is a front-end to brms and allows you to fit a different kind of beta regression that only needs 1 model formula (but can still use the endpoints of the scale):

Paper here: https://osf.io/preprints/socarxiv/2sx6y/

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