论文标题
零一膨胀的beta回归模型的应用来预测健康保险报销
An application of Zero-One Inflated Beta regression models for predicting health insurance reimbursement
论文作者
论文摘要
在精算实践中，合同限制（免赔额，共付额）和卫生保健支出之间的依赖性是通过蒙特卡洛模拟技术的应用来衡量的。为了实现相同的目标，我们提出了一种基于位置，规模和形状（GAMLSS）的通用线性模型的替代方法。我们专注于一年报销金额（在限制的影响之后）和一年支出（在限制效果之前）之间的比率估计。我们建议一个回归模型，以研究此响应变量与一组协变量之间的关系，例如限制和与健康风险有关的其他评估因素。通过这种方式，提供了报销和限制之间的依赖性结构。比率的密度函数是混合物分布，实际上，除了（0、1）之内的概率密度之外，它可以连续假设质量在0和1。这个随机变量不属于指数族，而普通的广义线性模型不合适。 GAMLSS引入了符合响应变量密度的概率结构，尤其是假定零一膨胀的β密度。后者是Bernoulli分布与Beta分布之间的混合物。
In actuarial practice the dependency between contract limitations (deductibles, copayments) and health care expenditures are measured by the application of the Monte Carlo simulation technique. We propose, for the same goal, an alternative approach based on Generalized Linear Model for Location, Scale and Shape (GAMLSS). We focus on the estimate of the ratio between the one-year reimbursement amount (after the effect of limitations) and the one year expenditure (before the effect of limitations). We suggest a regressive model to investigate the relation between this response variable and a set of covariates, such as limitations and other rating factors related to health risk. In this way a dependency structure between reimbursement and limitations is provided. The density function of the ratio is a mixture distribution, indeed it can continuously assume values mass at 0 and 1, in addition to the probability density within (0, 1) . This random variable does not belong to the exponential family, then an ordinary Generalized Linear Model is not suitable. GAMLSS introduces a probability structure compliant with the density of the response variable, in particular zero-one inflated beta density is assumed. The latter is a mixture between a Bernoulli distribution and a Beta distribution.
