Hi everyone,

I’ve been working on a couple of multinomial models, working on eye fixations. For a brief background, I would like to check where the subjects directed their first fixation across a series of trials. There are 4 possible targets, so I would like to estimate the probability that the first fixation would be directed to each target. The subjects belong to one of 5 different groups (different n in each).

For this, my understanding is that I need a model with variable intercept as follows (subjects are clustered in groups from the “strategy” variable):

```
y | trials(total) ~ 1 + (1 | strategy/subject)
```

Now, I would like to estimate the parameters for all the outcomes, which I think is accomplished by setting `refcat = NA`

in the `brm`

function.

Some other posts on the topic mentioned that using that setting, I should provide informative priors in order for the model to run properly. My question here would be, which one should I use?

I decided to use a skew_normal distribution centered at -1.0987, which in log odds is the equivalent to 25%, assuming that there is no difference in the allocation of fixations across the 4 targets. Also, I set the sd as a half cauchy distribution. The code looks like this:

```
first$y <- cbind(first$`1`, first$`2`, first$`3`, first$`4`)
first1.1 <- brm(data = first,
family = multinomial(refcat = NA,
link = logit),
formula = y | trials(total) ~ 1 + (1 | strategy/subject),
prior = c(prior(skew_normal(-1.0987, 2, 8), class = Intercept),
prior(skew_normal(-1.0987, 2, 8), class = Intercept, dpar = mu1),
prior(skew_normal(-1.0987, 2, 8), class = Intercept, dpar = mu2),
prior(skew_normal(-1.0987, 2, 8), class = Intercept, dpar = mu3),
prior(skew_normal(-1.0987, 2, 8), class = Intercept, dpar = mu4),
prior(cauchy(0, 2), class = sd, dpar = mu1),
prior(cauchy(0, 2), class = sd, dpar = mu2),
prior(cauchy(0, 2), class = sd, dpar = mu3),
prior(cauchy(0, 2), class = sd, dpar = mu4)
),
iter = 2000,
warmup = 500,
chains = 1,
cores = 1,
control = list(adapt_delta = 0.9)
)
```

I still get a warning after running it:

` Specifying global priors for regression coefficients in categorical models is deprecated and may not work as expected`

So I am wondering which other priors should I specify.

Finally, for checking the draws from the posterior for differences, I would like to compare each of the four targets to each other, to see if one of them shows a particular preference from the different groups. I am a little bit lost about what method would be more appropriate.

Thanks for your help.

**Copy of the data:**

first.csv (3.0 KB)