# Understanding multilevel multinomial models generated by brms

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?

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That looks correct to me.

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Thank you for the answer! I cannot explain the following behavior, where we study the difference between the probabilities of `c` and `a`:

``````library(bayesplot)
library(brms) # âš ď¸Ź Master on GitHub
library(tidyverse)

data <- tibble(a = seq(6) * 1000, b = 1000, c = seq(6) * 1000,
age = factor(seq(6))) %>%
mutate(total = a + b + c)
data\$counts <- with(data, cbind(a, b, c))

formula <- brmsformula(counts | trials(total) ~ (1 | age))
model <- brm(formula, data, multinomial(), seed = 42)

y <- with(data, (c - a) / total)
y_replica <- predict(model, newdata = data, summary = FALSE)
y_replica <- y_replica[ , , 'c'] - y_replica[ , , 'a']
y_replica <- sweep(y_replica, 2, data\$total, '/')
colnames(y_replica) <- seq(length(y))
mcmc_recover_intervals(y_replica, y)
``````

It looks like some kind of systematic error.

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Here is what is going on with `c` and `a` individually, respectively:

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I will check what is going wrong. The multinomial distribution is quite new to brms and there may be some problems still hiding somewhereâ€¦

Can you try again with the latest version from github which I pushed a few hours ago. With that version I get the expected results.

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Cannot thank you enough! It looks adequate now!

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:

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@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.