应用数学2017，Vol.30Issue(2)：457-468,12.
带有缺失数据的纵向隐马尔可夫因子模型的贝叶斯分析
Bayesian Analysis for Hidden Markov Factor Analysis Model with Missing Data Under Longitudinal Setting
摘要
Abstract
Hidden Markov Factor analytic models play an important role in characterizing interrelationships of multiple items and explaining the heterogeneity of multivariate longitudinal data.In practical application,data set often suffers from the missing problems.In this paper,we propose a parametric model for modeling the multivariate missing data under longitudinal setting.We use a multinomial model for the missing data indicators and propose a joint distribution for them,which can be written as a sequence of one-dimensional conditional distribution.Each one-dimensional conditional distribution not only depends on the current values of variables,but also incorporates the previous values and missing information.Within the Bayesian analysis framework,Markov Chains Monte Carlo method is used to implement posterior analysis.Gibbs sampler hybrid with Metropolis-Hastings algorithm is used to draw observations from the related full conditionals and posterior inferences are carried out based on these simulated observations.We conduct a simulation study.Empirical results show that the proposed method is rather effective when model is correctly specified and robust against model deviations.关键词
隐马尔可夫模型/因子分析模型/缺失机制/MCMC抽样/Gibbs抽样器Key words
Hidden Markov model/Factor analysis model/Missing data mechanism/MCMC sampling/Gibbs sampler分类
数理科学引用本文复制引用
夏业茂,陈宣..带有缺失数据的纵向隐马尔可夫因子模型的贝叶斯分析[J].应用数学,2017,30(2):457-468,12.基金项目
国家自然科学基金(11471161),南京市留学回国人员科技择优资助项目(013101001) （11471161）
