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Plenty of books about on GLMs for exponential families, but any good books or papers which study the Dirichlet distribution in particular?

kjetil b halvorsen
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Mari
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  • Tell us why you are using the Dirichlet distribution. – Michael R. Chernick Feb 12 '17 at 13:14
  • The response variable is a discrete probability distribution. – Mari Feb 12 '17 at 13:18
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    Possible duplicate of [Why Beta/Dirichlet Regression are not considered Generalized Linear Models?](https://stats.stackexchange.com/questions/304538/why-beta-dirichlet-regression-are-not-considered-generalized-linear-models) – kjetil b halvorsen Nov 26 '17 at 16:03
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    Ng, Tian and Tang, *Dirichlet and Related Distributions: Theory, Methods and Applications* – Mike Hunter Nov 26 '17 at 16:06
  • So why is it the Dirichlet distribution that is needed? Why not to estimate the parameters of a multinomial distribution? – Viktor Nov 26 '17 at 16:08
  • `"The response variable is a discrete probability distribution."` Discrete as in the result of Bionomial experiments? If that's the case, then you actually want the Multinomial GLM. – Firebug Jan 12 '18 at 17:35

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The book by Ludwig Fahrmeir Gerhard Tutz: "Multivariate Statistical Modelling Based on Generalized Linear Models (Second Edition)" contain some references, but it seems to be mostly to use of the dirichlet distribution as a prior distribution in multinomial logistic models. There are many papers on Dirichlet regression, see https://www.researchgate.net/profile/Rafiq_Hijazi/publication/228576713_Modelling_compositional_data_using_Dirichlet_regression_models/links/02e7e52e9cab9696f5000000.pdf or https://www.researchgate.net/profile/Rafiq_Hijazi/publication/265165887_Residuals_and_Diagnostics_in_Dirichlet_Regression/links/54054b8c0cf2c48563b13827.pdf . But are these models GLM's? see for instance Why Beta/Dirichlet Regression are not considered Generalized Linear Models?

kjetil b halvorsen
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  • What is the profit of using the Dirichlet distribution? Why are you not using, say, multinomial linear regression for the parameters of a categorical distribution itself? – Viktor Nov 26 '17 at 16:14
  • Do the categorical distributions of the response seem to be irregular? Why are Poisson regression or binomial regression or something alike not suitable? – Viktor Nov 26 '17 at 16:28
  • Please look through https://en.wikipedia.org/wiki/Multinomial_logistic_regression This is what I would start from. – Viktor Nov 27 '17 at 07:00