Hi everyone,

I fitted a model using brms using the following formula:

```
first1.1 <- brm(data = first,
family = multinomial(refcat = NA,
link = logit),
formula = y | trials(total) ~ 1 + (1 | strategy/subject))
```

I extracted samples from the posterior predictive distribution (I used `add_fitted_draws`

from the `tidybayes`

package , which is equivalent to `posterior_linpred`

). Now, I would like to test if the different levels of y follow a linear pattern. In the NHST I would perform a polynomial contrast to follow up, and I was wondering if this is possible here.

My approach so far was to transform the log odds into a standardized difference (by multiplying them by `sqrt(3)/pi`

and then I can do orthogonal coding on these values (-3, -1, 1, 3, since I have 4 levels here). Is this the right approach? I have seen the function `hypothesis`

is used for follow up comparisons between parameters, but I am not sure how to use it for orthogonal contrasts (if it’s possible at all).

My guess would be to weight all the samples from each of the levels by the orthogonal coding, add them up and then see if the result lies within a ROPE surrounding 0 (given that a linear contrast assumes equal difference between levels)?

Is this approach reasonable? Is there a more straightforward way of doing this?

Thanks for your help