Bayesian analysis of skew-normal independent linear mixed models with heterogeneity in the random-effects population |
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Authors: | Celso Rômulo Barbosa CabralVíctor Hugo Lachos Maria Regina Madruga |
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Institution: | a Departamento de Estatística, Universidade Federal do Amazonas, Brazil b Departamento de Estatística, IMECC, Universidade Estadual de Campinas, Brazil c Faculdade de Estatística, Universidade Federal do Pará, Brazil |
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Abstract: | We present a new class of models to fit longitudinal data, obtained with a suitable modification of the classical linear mixed-effects model. For each sample unit, the joint distribution of the random effect and the random error is a finite mixture of scale mixtures of multivariate skew-normal distributions. This extension allows us to model the data in a more flexible way, taking into account skewness, multimodality and discrepant observations at the same time. The scale mixtures of skew-normal form an attractive class of asymmetric heavy-tailed distributions that includes the skew-normal, skew-Student-t, skew-slash and the skew-contaminated normal distributions as special cases, being a flexible alternative to the use of the corresponding symmetric distributions in this type of models. A simple efficient MCMC Gibbs-type algorithm for posterior Bayesian inference is employed. In order to illustrate the usefulness of the proposed methodology, two artificial and two real data sets are analyzed. |
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Keywords: | Bayesian estimation Finite mixtures Linear mixed models MCMC Skew-normal distribution |
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