基于SAEM算法对缺失协变量的Logistic模型参数估计  

Parameter Estimation of Logistic Model with Missing Covariates Based on SAEM Algorithm

作　　者：刘玥 施三支[1] LIU Yue;SHI San-zhi(School of Science,Changchun University of Science and Technology,Changchun 130022)

机构地区：[1]长春理工大学理学院,长春130022

出　　处：《长春理工大学学报（自然科学版）》2021年第5期129-135,共7页Journal of Changchun University of Science and Technology(Natural Science Edition)

基　　金：国家自然科学基金(11601039);吉林省自然科学基金(20140101199JC)。

摘　　要：给出了Logistic模型中对缺失协变量数据的一种估计方法。将Marc Lavielle等人提出的SAEM算法进行了改进,引入Samiran Sinha等人提出的一种基于不可忽视机制基础上的NI-机制,以此来尽可能的利用数据中已存在的信息,并将其与现有处理缺失协变量较好的MCAR缺失机制下的半参数方法做对比研究。对Logistic模型的参数分别进行估计,对比分析这两种方法在不同缺失率下的优劣,并对最终结果进行回判,将回判准确率与标准误差作为判别标准。结果表明,当缺失率较小时,两者对缺失数据的处理性能都很好;但当缺失率较高时,半参数方法对数据的处理性能要优于SAEM算法。SAEM算法的运行速度始终快于半参数方法,缺失率较小时,用提出的SAEM算法做线上估计比半参数方法更具有优势。This paper presents an estimation method for missing covariates in logistic model.This paper improves the SAEM algorithm proposed by Marc lavielle and introduces a NI-mechanism based on the Non-ignorable mechanism proposed by samiran Sinha,so as to make use of the existing information in the data as much as possible,and compare it with the semiparametric method which is better to deal with missing covariates.The parameters of the logistic model are estimated respectively,and the advantages and disadvantages of the two methods under different missing rates are compared and analyzed.The final results are judged back,and the accuracy rate of the back judgment and standard error are used as the criteria.The results show that when the missing rate is low,the processing performance of both methods is very good;but when the missing rate is high,the semiparametric method is better than SAEM algorithm.The running speed of SAEM algorithm is always faster than that of semiparametric method,when the missing rate is small,The proposed SAEM algorithm has more advantages than semiparametric method in online estimation.

关 键 词：SAEM算法 NI-缺失机制 半参数方法 回判的准确率 

分 类 号：O212.1[理学—概率论与数理统计]