函数型累积Logistic回归模型研究与应用  

Research and application of functional cumulative Logistic regression model

作　　者：罗幼喜[1] 邓楠 胡超竹 李翰芳[1] LUO Youxi;DENG Nan;HU Chaozhu;LI Hanfang(School of Science,Hubei University of Technology,Wuhan,430068,China)

机构地区：[1]湖北工业大学理学院,武汉430068

出　　处：《华中师范大学学报（自然科学版）》2023年第2期185-194,共10页Journal of Central China Normal University：Natural Sciences

基　　金：国家自然科学基金青年基金项目(11701161);湖北省教育厅人文社科重点项目(20D043);湖北工业大学博士启动基金项目(BSQD2020103)。

摘　　要：该文针对响应变量为有序多分类标量数据,协变量为函数型数据构建函数型累积Logistic回归模型,并在贝叶斯分析框架下构造Gibbs抽样算法解决参数估计问题.具体解决流程为:首先,通过潜变量连接有序响应变量与函数协变量间的关系,同时对回归系数函数和回归函数型自变量选取主成分基函数进行展开,设置潜变量模型误差项服从Logistic分布.再利用Polya-Gamma变换解决模型似然函数的复杂性,并求得回归系数展开系数的后验分布从而构建Gibbs抽样算法.最后将该方法应用与模拟数据和实际空气质量指数(AQI)的分析,结果显示能较好地对模拟数据和空气质量指数(AQI)污染状况进行分类.In this paper,a functional cumulative Logistic regression model is constructed for the data whose response variable is an ordinal multi-classification index and covariables are functional index.Specific solution process is as follows:firstly,the relation between the ordinal response variable and functional covariables are connected through a latent variable.Meanwhile,the regression coefficient function and independent variable of regression are expanded by selected principal component basis function,and the error term is set to following a standard logistic distribution.Polya-Gamma transform then is used to solve the complexity of the likelihood function of the model,and the posterior distribution of the expansion coefficients is obtained to construct a Gibbs sampling algorithm.Finally,the proposed method is applied to the analysis of simulated data and an actual air quality index(AQI)data,and the results show that performance of new method are both better than traditional methods.

关 键 词：函数型数据 主成分分析 累积Logistic回归 Polya-Gamma变换 Gibbs抽样算法 

分 类 号：C81[社会学—统计学] O212[理学—概率论与数理统计]