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Robust Bayesian beta regression analysis
Journal of the Korean Data & Information Science Society 2018;29:27-36
Published online January 31, 2018
© 2018 Korean Data and Information Science Society.

Eun Jin Jang1 · Seongmi Choi2 · Dal Ho Kim3

1Department of Information Statistics, Andong National University
23Department of Statistics, Kyungpook National University
Correspondence to: Professor, Department of Statistics, Kyungpook National University, Daegu 41566, Korea. E-mail:
Received December 20, 2017; Revised January 7, 2018; Accepted January 8, 2018.
This is an Open Access article distributed under the terms of the Creative Commons Attribution Non-Commercial License ( which permits unrestricted non-commercial use, distribution, and reproduction in any medium, provided the original work is properly cited.
The beta regression model is adequate for situations where the continuous response variables with skewness and heteroscedasticity are restricted to the interval (0,1) such as percentages, proportions and fractions. The beta distribution can be parameterized in terms of its mean and precision parameter and the submodels for mean and precision can be estimated in beta regression. A common assumption in nonlinear mixed-effects models is the normality of random effects. However, the inferences are not robust in the presence of outliers. The scale mixtures of multivariate normal distribution include heavy-tailed distribution such as multivariate t-distribution and slash distribution and are often used for robust inference. In this paper, we proposed Bayesian hierarchical model using the scale mixtures of multivariate normal distribution as prior for random effects and applied to the real data.
Keywords : Beta density, beta regression, heteroskedasticity, mixed model, scale mixture.