Does any count-based compositional model (e.g. Dirichlet-multinomal) that allow category-wise variability exist?


I have created a differential-composition model (based on sum-constrained Beta-binomial) that allows

  • data count distribution
  • data compositionally
  • category-wise variability/concentration

I would like to know if I could claim that

“This is (to our knowledge?) the first available model that models data compositionality while allowing for category-wise variability”

Does anybody know if such a model already exists published somewhere?



I am not totally clear on what “category-wise variability/concentration” means, but it sounds like the generalised Dirichlet (-multinomial) distribution may be similar?


I mean in the sense that a Dirichlet distribution with 5 categories (k=5) has one (equivalent) degree of freedom for precision, while what I allow is 5 degrees of freedom for precision while capturing some compositional property of the data.

From browsing the literature is not immediately obvious, how many degrees of freedom there are for precision if k=5? (for example)

I believe that is one of the motivations behind the GD distribution. However it’s been a while so I’d trust reading a couple of papers on the topic rather than base your inferences on my recall of doing the same a few years ago.