From multi-category beta-binomial to multi-normal-logit-binomial


I implemented beta-binomial integrating multiple categories with a softmax of expected value. I need a beta-binomial because I need a category-level variance.

Does anyone have experience with replacing the beta distribution with multinormal-logit, to further model the correlation between categories (beyond the inverse correlation caused by the multinomial process)?

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I think the closest thing I’ve seen is the multivariate probit model (discussed e.g. here: Feedback request: Multivariate Probit Regression with GP) where some clever tricks are done to integrate out nuisance parameters that represent the latent multivariate normal.

I am not really sure I understand how multinomial sampling enters the picture as beta-binomial has binomial sampling. Could you be more specific about the generative process you have in mind?


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