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How can we check that the proportions are inflated at zero and one while using Beta Regression?

Aman Rastogi
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Beta regression assumes that the predicted variable is in $(0, 1)$, so exact $0$ and $1$ are excluded from the interval. So if you have any exact zeros, beta distribution and regression would not be appropriate and you would need to use something like the Hurdle model to account for them.

You may also be interested in reading the Dealing with 0,1 values in a beta regression thread.

Tim
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  • I somehow disagree... A hurdle model would assume a truncated Poisson/NB/Gaussian/etc. for the counts model so it would not allow for zeros either. So a hurdle model with Logistic/Beta for components should still be valid. No? – usεr11852 May 09 '21 at 13:29
  • We could run a hurdle model with Logistic/Beta for components should still be valid instead of a standard Logistic/Truncated_Poisson (that is the usual). – usεr11852 May 10 '21 at 09:09
  • @usεr11852 the only thing I'm saying is that the standard Bete regression model & common implementations would not work for data with exact 1 or 0. – Tim May 10 '21 at 09:34
  • Yes, of course, they shouldn't. But I am saying that "*Zero Inflated Beta Regression*" can be done through a hurdle model as it will naturally lend itself to Zero Inflated modelling. – usεr11852 May 10 '21 at 09:38
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    I think that the name "zero-inflated beta regression" is the source of the confusion here. While in "zero-inflated Poisson" you really **add** "excess" zeros to the zeros from the Poisson distribution, the same is not true for "zero-inflated beta". As beta regression cannot accomodate any zeros - as correctly pointed out by Tim - there is nothing to **inflate**. A better name would be "hurdle" or "two-part" model when adding zeros (and/or ones) to a standard beta regression. This is straightforward as correctly pointed out by user11852. – Achim Zeileis May 10 '21 at 09:38
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    @usεr11852 agree. I focused on the body of the question, asking about "inflated zeros in beta regression", but now I see how someone could focus more on the title of the question, than the body. Seems like the question is ambiguous. Edited for clarity. – Tim May 10 '21 at 09:56
  • @AchimZeileis You are too wise. Thank you. :) Tim, with you now, +1. – usεr11852 May 10 '21 at 11:41