带有不可忽略缺失数据的广义部分线性模型的贝叶斯分析

摘要

广义部分线性模型是广义线性模型和部分线性模型的推广,是一种应用广泛的半参数模型.本文讨论的是该模型在线性协变量和响应变量均存在非随机缺失数据情形下参数的Bayes估计和基于Bayes因子的模型选择问题,在分析过程中,采用了惩罚样条来估计模型中的非参数成分,并建立了Bayes层次模型;为了解决Gibbs抽样过程中因参数高度相关带来的混合性差以及因维数增加导致出现不稳定性的问题,引入了潜变量做为添加数据并应用了压缩Gibbs抽样方法,改进了收敛性;同时,为了避免计算多重积分,利用了M-H算法估计边缘密度函数后计算Bayes因子,为模型的选择比较提供了一种准则.最后,通过模拟和实例验证了所给方法的有效性.%As an extensive applied model, generalized partially linear model is an extension of generalized linear model and partially linear model. A method is proposed to obtain Bayesian estimation and to select appropriate model based on Bayes factor for such model with missing data both in covariate and response. Firstly, nonparametric components are fitted by penalized-splines and a Bayesian hierarchical model is set to model smooth parameters, then a vector of latent variable is introduced and the collapsed Gibbs sampler is implemented in order to improve the mixing and robustness of MCMC. Finally, simulation and real datasets are presented to illustrate the proposed methods.