Multinomial model in brms

Modeling
1

Hello Paul,
We were wondering if it was possible to estimate parameters using brms
for the following problem and data setup:
We have the following data

For each “Ethnicity” I have a count associated with the number of
copies of an Allele per Locus, call that y_{i,j} where i corresponds
to the Ethnicity and j corresponds to the Allele. We also have n_{i}
where it is simply the sum of the Allele per locus.

We are interested in estimating the following parameters:

  1. correlation of frequencies across Ethnicities,
  2. posterior estimates of Allele frequencies per Ethnicity.

According to your e-mail response:
you using a multinomal model.

So if A is the matrix containing the ethnicities in the rows (rows of the data) and the j allele in the columns, n is the total number of obs per row, and “obs” is a simple row index, you can go for something like

brm(A | trials(n) ~ 1 + <predictors> + (1 | ID | obs), ...)

The (1 | ID | obs) models a latent normal overdisperson (instead of a beta one as in the beta-binomial model)

and further the | ID | ensures that those are correlated across alleles.

My remaining question is what should ... be?

Best regards,
Manuel

1 Like
2

Hi Paul,

This is Yosuke, a trainee working with Maunel. For the model you’ve suggested, we ended up using this one:

fit <- brm(
    response | trials(n) ~ 1 + (1 | ID | obs),
    family=multinomial(),
    data=A,
    control=list(adapt_delta = 0.95)
)

We are trying to look at correlation across K alleles. It seems like the multinomial model estimates the correlation among K-1 parameters (which is natural in the multinomial setting), which we can extract with vcov.brmsfit(fit, correlation = TRUE).

For the visualization purpose, we are interested in showing correlation across K x K classes.
What would be the recommendation to recover the full correlation matrix?

Thank you very much for your help.

Sincerely yours,
Yosuke

3

Hi Paul,

We are trying to fit multinomial model using brms and it seems like we are not able to get a stable fit. We would love to get some advise.

Please see our Gist here: https://gist.github.com/yk-tanigawa/aeb3275bd7e93af009d39daed6cb8df9

Thank you very much.

Best,
Yosuke

4

vcov is not the right approach. The correlations you are looking for are shown in the summary output under group-level effects or alternatively extracted via VarCorr.

If you want estimates for the full correlation matrix you need to use family = multinomial(refcat = NA) but be aware that this implies a very hard to fit model which requires informative priors to run well enough.

5

Thank you, so much!

6

Thank you very much! We will have a look.