基于Bootstrap方法的对数线性模型构建  

Logarithmic Linear Model Construction under Bootstrap

作　　者：徐玲丽 陈雪东[2] 

机构地区：[1]浙江师范大学数理信息与工程学院,浙江金华321004 [2]湖州师范学院理学院,浙江湖州313000

出　　处：《湖州师范学院学报》2017年第10期1-5,共5页Journal of Huzhou University

基　　金：国家自然科学基金项目(1171105)

摘　　要：对于不易进行数据收集的分类变量,通常得到的样本是有限的.如果仅用这些数据构建变量间的对数线性模型往往缺乏可靠性,而且对各交互项的参数估计精度可能较低.针对该问题,提出先用Bootstrap抽样法产生多份一定量的数据集,分别模拟它们的对数线性模型,得到模型各个参数的估计向量,然后对所有参数的估计向量进行聚类,得到若干份各参数估计的向量.实验结果表明,即使各参数与真实模型的各个参数有差异,这若干个参数估计向量对应的模型的概率分布与真实模型的概率分布的K-L距离都较小,即概率分布很接近,并且在这若干个向量中,越靠近对应参数的置信区间,它与真实的概率分布的K-L距离越小.Since it is difficult to collect data of the limited. So it is unreliable to construct the logarithmic categorical variables, the commonly obtained samples are linear model between variables with these data, and the parameter estimation accuracy of each interaction item may be very low. A number of data sets are generated by sampling method, and their logarithmic linear model are simulated respectively so that the estimated vectors of the parameters of the model are obtained, and the estimation vectors of all the parameter are clustered to obtain a number of parameters. The experimental results show that even if the parameters of each parameter are differ- ent from those of the real model, the probability distribution of the model corresponding to the parameter esti- mation vector is smaller than the probability distribution of the real model, that is, the probability distribution is close. In the vector, the closer the confidence interval of the corresponding parameter is, the smaller the distance from the true probability distribution will be.

关 键 词：分类变量 对数线性模型 Bootstrap抽样 聚类 K-L距离 置信区间 

分 类 号：O212[理学—概率论与数理统计]