Bayesian quantile regression for skew-normal linear mixed models
Linear mixed models have been widely used to analyze repeated measures data which arise in many studies. In most applications, it is assumed that both the random effects and the within-subjects errors are normally distributed. This can be extremely restrictive, obscuring important features of within...
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| Published in | Communications in statistics. Theory and methods Vol. 46; no. 22; pp. 10953 - 10972 |
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| Main Authors | , |
| Format | Journal Article |
| Language | English |
| Published |
Philadelphia
Taylor & Francis
17.11.2017
Taylor & Francis Ltd |
| Subjects | |
| Online Access | Get full text |
| ISSN | 0361-0926 1532-415X |
| DOI | 10.1080/03610926.2016.1257713 |
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| Abstract | Linear mixed models have been widely used to analyze repeated measures data which arise in many studies. In most applications, it is assumed that both the random effects and the within-subjects errors are normally distributed. This can be extremely restrictive, obscuring important features of within-and among-subject variations. Here, quantile regression in the Bayesian framework for the linear mixed models is described to carry out the robust inferences. We also relax the normality assumption for the random effects by using a multivariate skew-normal distribution, which includes the normal ones as a special case and provides robust estimation in the linear mixed models. For posterior inference, we propose a Gibbs sampling algorithm based on a mixture representation of the asymmetric Laplace distribution and multivariate skew-normal distribution. The procedures are demonstrated by both simulated and real data examples. |
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| AbstractList | Linear mixed models have been widely used to analyze repeated measures data which arise in many studies. In most applications, it is assumed that both the random effects and the within-subjects errors are normally distributed. This can be extremely restrictive, obscuring important features of within-and among-subject variations. Here, quantile regression in the Bayesian framework for the linear mixed models is described to carry out the robust inferences. We also relax the normality assumption for the random effects by using a multivariate skew-normal distribution, which includes the normal ones as a special case and provides robust estimation in the linear mixed models. For posterior inference, we propose a Gibbs sampling algorithm based on a mixture representation of the asymmetric Laplace distribution and multivariate skew-normal distribution. The procedures are demonstrated by both simulated and real data examples. |
| Author | Meshkani, M. R. Aghamohammadi, A. |
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| CitedBy_id | crossref_primary_10_1080_03610918_2018_1484482 crossref_primary_10_1080_03610926_2022_2150054 crossref_primary_10_1007_s40300_018_0136_4 crossref_primary_10_1080_14737167_2021_1857242 |
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| SubjectTerms | Asymmetric laplace distribution Bayesian analysis Bayesian quantile regression Computer simulation Economic models linear mixed models MCMC Normal distribution Normality Regression analysis skew-normal distribution Skewed distributions Statistical analysis |
| Title | Bayesian quantile regression for skew-normal linear mixed models |
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