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تسجيل مستخدم جديدThe Integrated nested Laplace approximation for fitting models with multivariate response
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نشر من قبل
Joaqu\\'in Mart\\'inez-Minaya
تاريخ النشر
2019
مجال البحث
الاحصاء الرياضي
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English
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This paper introduces a Laplace approximation to Bayesian inference in regression models for multivariate response variables. We focus on 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 this 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 INLA package, which can not deal directly with multivariate likelihoods like the Dirichlet likelihood. Simulation studies are presented to validate the good behaviour of the proposed method, while a real data case-study is used to show how this approach can be applied.
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