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