广义泊松回归模型的推广及其在医疗保险中应用  

Generalization of Generalized Poisson Regression Model and Its Medicare Application

作　　者：徐昕[1] XU Xin(School of Finance, Capital University of Economics and Business, Beijing 100070, China)

机构地区：[1]首都经济贸易大学金融学院,北京100070

出　　处：《数理统计与管理》2017年第2期215-225,共11页Journal of Applied Statistics and Management

基　　金：2015年中国保监会部级课题项目支持;国家社会科学基金项目(12CJY114)支持

摘　　要：计数数据往往存在过离散(over-dispersed)即方差大于均值特征,若利用传统的泊松回归模型拟合数据往往会导致其参数的标准误差被低估,显著性水平被高估的错误结论。负二项回归模型、广义泊松回归模型通常被用来处理过离散特征数据。本文以两类广义泊松回归模型GP-1和GP-2模型为基础,将其推广为更为一般的GP-P形式,其中P为参数。此时,P=1或P=2,GP-P模型就退化为GP-1和GP-2模型。文中最后利用此类推广的GP-P模型处理了一组医疗保险数据,并与泊松回归模型、负二项回归模型拟合结果进行了比较。结果表明,推广后的GP-P模型的拟合效果更优。Count data are often over-dispersed,that is variance greater than mean.When count data appear to be over-dispersed,continue using Poisson regression models may underestimate the parameters of standard errors and overestimate the significance level,which eventually leads to incorrect inference.Negative binomial regression model and generalized Poisson regression model are usually used to fit overdispersed data.This paper extends the usual two types of generalized Poisson regression models GP-1and GP-2 to more general formal GP-P.When P = 1 or P = 2,the GP-P model will degenerate to the GP-1 and GP-2 models.Different models of Poisson model,negative binomial models and generalized Poisson models were fit to the Medicare data.The results show that the extended generalized Poisson model（GP-P） model effectively improves the goodness-of-fit.

关 键 词：泊松回归 负二项回归 广义泊松回归 过离散 

分 类 号：O212[理学—概率论与数理统计]