The Integrated Nested Laplace Approximation for fitting Dirichlet regression models

Joaquín Martínez-Minaya*, Finn Lindgren, Antonio López-Quílez, Daniel Simpson, David Conesa

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

This paper introduces a Laplace approximation to Bayesian inference in Dirichlet regression models, which can be used to analyze a set of variables on a simplex exhibiting skewness and heteroscedasticity, without having to transform the data.
These data, which mainly consist of proportions or percentages of disjoint categories, are widely known as compositional data and are common in areas such as ecology, geology, and psychology. We provide both the theoretical foundations and a description of how Laplace approximation can be implemented in the case of Dirichlet regression.
The paper also introduces the package dirinla in the R-language that extends the RINLA package, which can not deal directly with Dirichlet likelihoods. Simulation studies are presented 16 to validate the good behaviour of the proposed method, while 17 a real data case-study is used to show how this approach can be applied.
Original languageEnglish
JournalJournal of Computational and Graphical Statistics
Early online date8 Nov 2022
DOIs
Publication statusE-pub ahead of print - 8 Nov 2022

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