COVID-19病死率模型的参数分位数β回归
A parametric quantile beta regression for modeling case fatality rates of COVID-19
摘要：
受COVID-19病死率（CFR）的启发，本文基于广义三参数贝塔（GB 3）分布建立了一个全参数分位数回归模型。Beta回归模型主要用于对比率和比例进行建模。然而，这些模型通常是指定的条件平均值。因此，如果观察到的响应变量遵循非对称分布（如CFR数据），则这些数据可能不充分。此外，β回归模型不考虑协变量在因变量范围内的影响，这可以通过条件分位数方法来实现。为了引入所提出的GB 3回归模型，我们首先通过插入分位数参数来重新参数化GB 3分布，然后我们开发了新提出的分位数模型。我们还提出了一个简单的解释预测响应关系的百分位数的增加/减少。进行蒙特卡罗研究以评估最大似然估计的性能和链接函数的选择。最后，来自智利的一个真实的COVID-19数据集进行了分析和讨论，以说明所提出的方法。
英文摘要：
Motivated by the case fatality rate (CFR) of COVID-19, in this paper, we develop a fully parametric quantile regression model based on the generalized three-parameter beta (GB3) distribution. Beta regression models are primarily used to model rates and proportions. However, these models are usually specified in terms of a conditional mean. Therefore, they may be inadequate if the observed response variable follows an asymmetrical distribution, such as CFR data. In addition, beta regression models do not consider the effect of the covariates across the spectrum of the dependent variable, which is possible through the conditional quantile approach. In order to introduce the proposed GB3 regression model, we first reparameterize the GB3 distribution by inserting a quantile parameter and then we develop the new proposed quantile model. We also propose a simple interpretation of the predictor-response relationship in terms of percentage increases/decreases of the quantile. A Monte Carlo study is carried out for evaluating the performance of the maximum likelihood estimates and the choice of the link functions. Finally, a real COVID-19 dataset from Chile is analyzed and discussed to illustrate the proposed approach.
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