Beta regression is frequently used when the outcome variable y is bounded within a specific interval, transformed to the (0, 1) domain if necessary. However, standard beta regression cannot handle data observed at the boundary values of 0 or 1, as the likelihood function takes on values of either 0 or infinity. To address this issue, we propose the Scale-Location-Truncated beta (SLTB) regression model, which extends the beta distribution's domain to the [0, 1] interval. By using scale-location transformation and truncation, SLTB distribution allows positive finite mass to the boundary values, offering a flexible approach for handling values at 0 and 1. In this paper, we demonstrate the effectiveness of the SLTB regression model in comparison to standard beta regression models and other approaches like the Zero-One Inflated Beta (ZOIB) mixture model and XBX regression. Using empirical and simulated data, we compare the performance including predictive accuracy of the SLTB regression model with other methods, particularly in cases with observed boundary data values for y. The SLTB model is shown to offer great flexibility, supporting both linear and nonlinear relationships. Additionally, we implement the SLTB model within maximum likelihood and Bayesian frameworks, employing both hierarchical and non-hierarchical models. These comprehensive implementations demonstrate the broad applicability of SLTB model for modeling data with bounded values in a variety of contexts.

翻译：当结果变量y被限定在特定区间内（必要时可变换至(0, 1)域）时，Beta回归是常用的方法。然而，标准Beta回归无法处理在边界值0或1处观测到的数据，因为其似然函数会取值为0或无穷大。为解决此问题，我们提出了尺度-位置-截断Beta（SLTB）回归模型，该模型将Beta分布的定义域扩展至[0, 1]区间。通过尺度-位置变换与截断处理，SLTB分布允许边界值具有正有限概率质量，为处理0和1处的数值提供了灵活的方法。本文通过实证与模拟数据，将SLTB回归模型与标准Beta回归模型及其他方法（如零一膨胀Beta混合模型与XBX回归）进行比较，特别是在y存在观测边界值的情况下，评估了包括预测准确性在内的各项性能。研究表明，SLTB模型具有高度灵活性，可同时支持线性与非线性关系。此外，我们在极大似然与贝叶斯框架下实现了SLTB模型，并采用了分层与非分层模型。这些全面实现证明了SLTB模型在各种情境下对具有边界值数据的建模具有广泛适用性。