Beta regression models are commonly used in the case of a dependent variable y that exists on the range (0,1). However, when y can additionally take on the values of zero and/or one, limitations of the beta distribution and beta regression models become apparent. One recent approach is to use an inflated beta regression model which has discrete point-valued components. In this article, we introduce a new class of regression models for y ∈ [0,1] that is fully continuous. This allows the entirety of y to be treated as a continuum instead of discontinuously, which appears to be a new development for the literature. We use a Bayesian approach for estimation. We also illustrate the impact of different choices of prior distributions on empirical findings and perform a simulation study examining model fit.

中文翻译：

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倾斜 Beta 分布的回归建模：贝叶斯方法

Beta 回归模型通常用于因变量y存在于 (0,1) 范围内的情况。然而，当y可以另外取零和/或一的值时，beta 分布和 beta 回归模型的局限性变得明显。最近的一种方法是使用具有离散点值组件的膨胀 beta 回归模型。在本文中，我们介绍了一类新的 完全连续的y ∈ [0,1]回归模型。这允许整个y被视为连续体而不是不连续体，这似乎是文学的新发展。我们使用贝叶斯方法进行估计。我们还说明了先验分布的不同选择对经验发现的影响，并进行了模拟研究检查模型拟合。