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The "supplementary material" on the page below discusses the issue :

http://supp.apa.org/psycarticles/supplemental/met_11_1_54/met_11_1_54_supp.html

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What do you mean by problems? The beta distribution's support exists on [0,1], including the boundary values. Often estimation, as regards to regression, is done by maximizing unknown parameter values on the Real scale, thus using a transformation, such as a logit or probit link so that boundary issues in the estimation process are removed. See http://cran.r-project.org/web/packages/betareg/vignettes/betareg.pdf

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Brian, logit or probit transform does not help much when you have samples sitting right on the boundaries ; as your references points out :

"Furthermore, if y also assumes the extremes 0 and 1, a useful transformation in practice is (y · (n − 1) + 0.5)/n where n is the sample size (Smithson and Verkuilen 2006)."

(which is the reference I gave above)

However, this always seemed to me more like a "quick and not so dirty trick" than a clean theoretically grounded approach. I would be quite curious to learn about a cleaner treatment.

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Dear Clerot Fabrice thank you so much for your attention and helpful document.

Dear Brian Gerber, the problem is an error which will be appear when implementing optimization commands (R Optim's or nlminb's) for estimating the parameters of beta distribution in the presence of 0 or 1.

Impact Factor is about the journal as a whole and may not truly reflect the impact of individual papers in that journal, where as h-index is about the individual so i will prefer h-index over IF

If the data comes exactly from a beta distribution on [0, 1] the values 0 and 1 themselves can never occur. If you do have 0's or 1's, your model is inappropriate. You had better think up a model which respects this feature of the data. Eg the data is rounded to a small number of digits after the decimal point - then you essentially have grouped data from a beta distribution.

Dear Leila,

as mentioned by R.D. Gill, an important point is whether the zeroes or ones you have in your sample are essential (true 0 or 1) or they are "under detection limit". In the first case, the beta model is unappropriate. Under detection limit data are a special kind of censored compositional data. There are methods to replace these zeroes (the ones correspond to zeroes of the complementary part) or to make multiple imputations in the framework of compositional data analysis. I would recommend to have a look on the contributions by J.A. Martin-Fernandez and J. Palarea, as they are specialists on this topic.

However, from the compositional point of view, we recommend to fit more flexible distributions than the Beta-Dirichlet distribution. The alternative is the normal distribution on the simplex (also known as logistic-normal or logit-normal). However, the problem with the zeroes is still the same as in the beta distribution.

Dear Professor Juan Jose Egozcue

Thank you so much for your note and advise.

I will study the reference that you recommend.

Best regards,

Leila Delgarm.