paul-buerkner/brms

Implement the zero-inflated dirichlet distribution

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#722 opened on Aug 5, 2019

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Description

Dirichlet regression is possible in brms using the dirichlet family. But this requires that outcomes be non-zero.

Election outcomes are one case where outcomes are distributed according to the dirichlet distribution (on the probability scale and sum to 1), but that exhibit considerable zero-inflation. This is often true where parties do not stand for whatever reason.

Rather than fudge this by replacing 0 with a tiny number, it would be good to be able to model the zero-inflation. Effectively, this would be a multinomial extension of the zero-inflated beta distribution in the same way that the dirichlet distribution is a multinomial extension of the standard beta distribution.

At present, this is possible using the zadr() function in the Compositional package. But this lacks a lot of functionality and is Frequentist, not Bayesian.

An accompanying paper for the Compositional package is available here. There is also another good paper detailing zero-inflated dirichlet regression in the context of microbiome data here.

Contributor guide

Tech stack
None
Domain
datamachine learning
Issue type
feature
DifficultyEstimated implementation difficulty for a new contributor, from 1 for very small changes to 5 for expert-level work.
5
Estimated timeA rough time range for an experienced contributor to investigate, implement, test, and prepare a pull request.
over 1 week
Activity statusHow available the issue appears right now: fresh, active, stale, blocked, or waiting on maintainer input.
stale
ClarityHow clearly the issue explains the expected change, acceptance criteria, and next step.
clear
Prerequisites
R programmingDirichlet distributionBayesian statisticsbrms package internals
Newbie friendlinessA 1-100 score estimating how approachable this issue is for first-time contributors.
10
Research direction
Study the zero inflated Dirichlet distribution as described in the referenced papers (Tsagris et al. 2014 and Chen & Li 2018). Examine the existing 'dirichlet' family in brms (likely in 'brm.R' or similar) to understand the current implementation. Look at the 'zadr()' function in the Compositional package for R code. The goal is to add a new family (e.g., 'zero inflated dirichlet') to brms that models zero inflated Dirichlet outcomes. Consider extending the 'dirichlet' family or creating a custom Stan code block. Check the brms issue #722 for discussion on the approach.