Dirichlet negative multinomial regression


I am using a dirichlet-multinomial regression model. However I see that quite tidy associations for low-count categories don’t get picked up, essentially because the overall variance is quite high (I assume skewed by abundant categories).

For example (! I am plotting proportions here, but the data is actually in counts)

The yellow highlight category would rather seem associated with the x axis covariate.


I was wondering if anybody had experience with Dirichlet negative multinomial regression, where each category can have different overdispersions, but the counts across categories are correlated (sum to 100%)

E.g. https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3590929/

Or even a simple Dirichlet negative multinomial would do

Any experience around?