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

  • $\begingroup$ Tell us why you are using the Dirichlet distribution. $\endgroup$ Feb 12 '17 at 13:14
  • $\begingroup$ The response variable is a discrete probability distribution. $\endgroup$
    – Mari
    Feb 12 '17 at 13:18
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    $\begingroup$ Possible duplicate of Why Beta/Dirichlet Regression are not considered Generalized Linear Models? $\endgroup$ Nov 26 '17 at 16:03
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    $\begingroup$ Ng, Tian and Tang, Dirichlet and Related Distributions: Theory, Methods and Applications $\endgroup$ Nov 26 '17 at 16:06
  • $\begingroup$ So why is it the Dirichlet distribution that is needed? Why not to estimate the parameters of a multinomial distribution? $\endgroup$
    – Viktor
    Nov 26 '17 at 16:08

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?

  • $\begingroup$ 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? $\endgroup$
    – Viktor
    Nov 26 '17 at 16:14
  • $\begingroup$ Do the categorical distributions of the response seem to be irregular? Why are Poisson regression or binomial regression or something alike not suitable? $\endgroup$
    – Viktor
    Nov 26 '17 at 16:28
  • $\begingroup$ Please look through en.wikipedia.org/wiki/Multinomial_logistic_regression This is what I would start from. $\endgroup$
    – Viktor
    Nov 27 '17 at 7:00

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