Bayesian Regression for a Dirichlet Distributed Response using Stan
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For an observed response that is composed by a set - or vector - of positive values that sum up to 1, the Dirichlet distribution (Bol'shev, 2018) is a helpful mathematical construction for the quantification of the data-generating mechanics underlying this process. In applications, these response-sets are usually denoted as proportions, or compositions of proportions, and by means of covariates, one wishes to manifest the underlying signal - by changes in the value of these covariates - leading to differently distributed response compositions. This article gives a brief introduction into this class of regression models, and based on a recently developed formulation (Maier, 2014), illustrates the implementation in the Bayesian inference framework Stan.
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