Ancestors

Written by Achim Zeileis on 2024-09-16 at 08:02

📢 PSA: Tired of #betareg in :rstats: complaining when you have 0 and/or 1 in your response variable?

🎉 Good news: betareg can now capture this at the expense of a single extra parameter! #rstats

📄 New arXiv working paper with @ikosmidis

https://www.zeileis.org/news/xbx/

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Written by Facundo Muñoz on 2024-09-18 at 13:27

@zeileis @ikosmidis

Genius!! very elegant and clever solution. 👏👏

Would the same idea be applicable to Poisson or negative-binomial #regression with non-negative outcomes?

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Written by Achim Zeileis on 2024-09-18 at 14:26

@famuvie @ikosmidis I think it's the other way around: For XBX we also took inspiration from zero-inflated and hurdle count data models.

But for count data the situation is a bit different because you always have a point mass at zero. So it's just the question how to inflate (or modify) that.

In contrast the beta distribution has no probability weight on the boundaries. Hence the extended-support approach.

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Toot

Written by Facundo Muñoz on 2024-09-18 at 15:35

@zeileis @ikosmidis Right, I meant regression with continuous likelihood like Gamma.

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Descendants

Written by Achim Zeileis on 2024-09-18 at 15:56

@famuvie @ikosmidis Yes, there is some work in that direction. For example, Baran & Nemoda proposed to use a censored shifted gamma distribution for modeling precipitation (non-negative with point mass at zero).

But I haven't tried how reliably their exceedence parameter can be estimated in practice (without shrinkage towards zero).

https://doi.org/10.1002/env.2391

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Written by Facundo Muñoz on 2024-09-18 at 17:18

@zeileis @ikosmidis Thanks! This shrinkage idea is interesting, but defies my intuition. How in the world is a hyperparameter more easily identifiable than the parameter itself? 🤯

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Written by Achim Zeileis on 2024-09-19 at 06:18

@famuvie @ikosmidis The exceedence parameters in the XB and the XBX distribution play very similar roles. I wouldn't think of it as a hyperparameter, really. Both parameters drive how much probability mass is in the tails of the latent distribution, outside of [0, 1], which then becomes the point masses at 0 and 1.

However, in XBX the support of the latent distribution does not depend on ν which makes the marginal likelihood and its derivates much more well-behaved.

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