Department of Statistics, University of Pretoria, Pretoria, South Africa.
Faculty of Mathematical Sciences, Department of Statistics, Shahrood University of Technology, Shahroud, Iran.
Stat Methods Med Res. 2019 Dec;28(12):3729-3740. doi: 10.1177/0962280218814574. Epub 2018 Nov 25.
Real phenomena often leads to challenges in data. One of these is outliers or influential values. Especially in a small sample, these values can have a major influence on the modeling process. In the beta regression framework, this issue has been addressed mainly in two ways: the assumption of a different response model and the application of a minimum density power divergence estimation (MDPDE) procedure. In this paper, however, we propose a simple hierarchical Bayesian methodology in the context of a varying dispersion beta response model that is robust to outliers, as shown through an extensive simulation study and analysis of two real data sets. To robustify Bayesian modeling, a heavy-tailed Student's t prior with uniform degrees of freedom is adopted for the regression coefficients. This proposal results in a wieldy implementation procedure which avails practical use of the approach.
实际现象往往会给数据带来挑战。其中之一是异常值或有影响的值。特别是在小样本中，这些值可能会对建模过程产生重大影响。在贝塔回归框架中，这个问题主要通过两种方法来解决：假设不同的响应模型和应用最小密度幂离差估计（MDPDE）程序。然而，在本文中，我们提出了一种简单的分层贝叶斯方法，即在变分散β响应模型的背景下，该方法对异常值具有鲁棒性，这通过广泛的模拟研究和两个真实数据集的分析得到了证明。为了使贝叶斯建模稳健，我们采用具有均匀自由度的重尾学生 t 先验对回归系数进行建模。这一建议产生了一个易于实施的程序，便于该方法的实际应用。
