I would like to check my understanding of multilevel models generated by brms for the case of the multinomial family and would appreciate any comments.

Suppose there are three categories: a, b, and c. Suppose also there is one grouping factor: age. The formula is as follows:

y | trials(total) ~ (1 | age)

where y binds counts for a, b, and c (in that order), and total is the total number of trials for the corresponding observations.

Would the following be a correct summary of the model being generated?

For those who happen to stumble upon this question and would like to know more, here is an article, I have written, describing this very model applied to a real-world problem:

@IvanUkhov Your summary of multilevel multinomial using brms is very helpful! I am wondering If you or anyone else on the listserve has an example with repeated measures that I could work through to help me understand how I might adapt this kind of model to an experiment where dependent variable is 3 category choice that is repeated 60 times under different conditions.