POISSON平均极大似然中心惩罚估计初探  

A preliminary study on Poisson average maximum likelihood-centered penalized estimation

作　　者：蒋晓红 曾晶[2] 李胜 张华东[3] 邓颖[2] 殷菲 JIANG Xiao-hong;ZENG Jing;LI Sheng;ZHANG Hua-dong;DENG Ying;YIN Fei(West China School of Public Health and West China Fourth Hospital,Sichuan University,Chengdu,Sichuan 610041,China;不详)

机构地区：[1]四川大学华西公共卫生学院/华西第四医院,四川成都610041 [2]四川省疾病预防控制中心,四川成都610041 [3]重庆市疾病预防控制中心

出　　处：《现代预防医学》2023年第7期1165-1170,1192,共7页Modern Preventive Medicine

基　　金：国家自然科学基金(81872713,81803332);四川省科学技术厅重点研发项目(2021YFS0181);重庆市科技局资助(cstc2020jscx-cylhX0003)。

摘　　要：目的为了控制多重共线性在泊松回归中带来的不利影响,本研究提出泊松平均极大似然中心惩罚估计(Poisson average maximum likelihood-centered penalized estimation,PAMLPE),并对该方法参数估计表现进行评估。方法本研究基于均值最小二乘中心化惩罚回归(average OLS-centered penalized regression,AOPR)思想提出PAMLPE。利用模拟研究生成不同场景的数据集,采用极大似然估计、泊松岭回归估计(Poisson ridge estimation,PRE)以及PAMLPE建立回归模型,计算各个模型的mean squared error(MSE)和predictive MSE(PMSE)并进行比较,进而评估PAMLPE参数估计的准确性、模型预测表现以及适用场景。结果绝大多数模拟场景(94%)中PAMLPE的表现优于极大似然估计,在大多数βs符号相同的模拟场景(62.5%)中,PAMLPE参数估计值比PRE更加准确,自变量个数增加,MSE的改善效果明显增加且更加稳定,最大为80.6%,但在大多数βs符号不同的模拟场景中(74.5%),PRE参数估计值更加准确。结论PAMLPE能有效处理泊松回归中多重共线性问题,尤其是当βs符号相同时,PAMLPE处理效果优于PRE。Objective To control the negative effects of multicollinearity in the Poisson regression model,we developed a novel penalty regression method,Poisson average maximum likelihood-centered penalized estimation(PAMLPE),and evaluated the performance of this method.Methods Based on the idea of average OLS-centered penalized regression(AOPR),we proposed PAMLPE.Through simulation studies,we applied maximum likelihood estimation,Poisson ridge estimation(PRE),and PAMLPE to establish regression models.Mean squared error(MSE)and predictive MSE(PMSE)of these models were calculated and compared to evaluate the accuracy of PAMLPE estimators,the model prediction performance,and the applicable situations.Results PAMLPE performed better than maximum likelihood estimation in most situations(94%)and obtained more accurate estimators than PRE when the signs of trueβs were identical(62.5%).Especially when the number of independent variables increased,the improvement of MSE increased significantly and became more stable,with a maximum improvement of 80.6%.However,the PRE parameter estimates were more accurate in most simulations where the trueβs signs were different(74.5%).Conclusion PAMLPE can effectively address multicollinearity in Poisson regression,especially whenβs signs are the same,and PAMLPE is better than PRE in processing multicollinearity.

关 键 词：PAMLPE 多重共线性 泊松惩罚回归 收缩中心 

分 类 号：O212.1[理学—概率论与数理统计]