标题： 具有参数化链接函数的可变分散Beta回归模型 显示英文标题

标题： Variable dispersion beta regressions with parametric link functions

摘要： 本文提出了一类新的回归模型，用于限制在区间$(0,1)$内的连续数据，例如比率和比例。 所提出的模型类别假设感兴趣变量服从 beta 分布，并且具有针对均值和离散参数的回归结构。 这些结构考虑了协变量、未知回归参数以及参数化链接函数。 链接函数依赖于建模随机成分与线性预测器之间关系的参数。 对称和非对称 Aranda-Ordaz 链接函数进行了详细讨论。 根据参数值，这些链接函数对应固定链接（如逻辑斯蒂和互补对数-对数函数）的特殊情况。 通过最大似然方法同时估计回归和链接函数参数。 给出了得分函数和费雪信息矩阵的闭式表达。 讨论了大样本推断方面的问题，并提出了一些诊断措施。 使用蒙特卡洛模拟研究评估点估计量在有限样本下的表现。 最后，展示并讨论了一个使用真实数据的实际应用。 显示英文摘要

摘要： This paper presents a new class of regression models for continuous data restricted to the interval $(0,1)$, such as rates and proportions. The proposed class of models assumes a beta distribution for the variable of interest with regression structures for the mean and dispersion parameters. These structures consider covariates, unknown regression parameters, and parametric link functions. Link functions depend on parameters that model the relationship between the random component and the linear predictors. The symmetric and assymetric Aranda-Ordaz link functions are considered in details. Depending on the parameter values, these link functions refer to particular cases of fixed links such as logit and complementary log-log functions. Joint estimation of the regression and link function parameters is performed by maximum likelihood. Closed-form expressions for the score function and Fisher's information matrix are presented. Aspects of large sample inferences are discussed, and some diagnostic measures are proposed. A Monte Carlo simulation study is used to evaluate the finite sample performance of point estimators. Finally, a practical application that employs real data is presented and discussed.