Instituto de Matemática e Estatística, Universidade de São Paulo, São Paulo, SP, Brazil.
Departamento de Estadística, Universidad Nacional de Colombia, Bogotá, Colombia.
PLoS One. 2022 Nov 3;17(11):e0276695. doi: 10.1371/journal.pone.0276695. eCollection 2022.
In many practical situations, there is an interest in modeling bounded random variables in the interval (0, 1), such as rates, proportions, and indexes. It is important to provide new continuous models to deal with the uncertainty involved by variables of this type. This paper proposes a new quantile regression model based on an alternative parameterization of the unit Burr XII (UBXII) distribution. For the UBXII distribution and its associated regression, we obtain score functions and observed information matrices. We use the maximum likelihood method to estimate the parameters of the regression model, and conduct a Monte Carlo study to evaluate the performance of its estimates in samples of finite size. Furthermore, we present general diagnostic analysis and model selection techniques for the regression model. We empirically show its importance and flexibility through an application to an actual data set, in which the dropout proportion of Brazilian undergraduate animal sciences courses is analyzed. We use a statistical learning method for comparing the proposed model with the beta, Kumaraswamy, and unit-Weibull regressions. The results show that the UBXII regression provides the best fit and the most accurate predictions. Therefore, it is a valuable alternative and competitive to the well-known regressions for modeling double-bounded variables in the unit interval.
在许多实际情况下,人们对在区间(0,1)中建模有界随机变量(如速率、比例和指数)感兴趣。提供新的连续模型来处理这类变量所涉及的不确定性非常重要。本文提出了一种新的基于单位 Burr XII(UBXII)分布的替代参数化的分位数回归模型。对于 UBXII 分布及其相关回归,我们得到了得分函数和观测信息矩阵。我们使用最大似然法来估计回归模型的参数,并进行了蒙特卡罗研究,以评估其在有限大小样本中的估计的性能。此外,我们还为回归模型提供了一般诊断分析和模型选择技术。我们通过对巴西本科动物科学课程辍学比例的实际数据集的应用,实证证明了其重要性和灵活性。我们使用统计学习方法将提出的模型与 beta、Kumaraswamy 和单位 Weibull 回归进行比较。结果表明,UBXII 回归提供了最佳拟合和最准确的预测。因此,它是一种有价值的替代方法,也是在单位区间内对双边界变量进行建模的著名回归方法的竞争对手。