评价多水平因子分析模型的异质性:半参数贝叶斯方法  

Assessing Heterogeneity in Multilevel Factor Analysis Model:A Semiparametric Bayesian Approach

作　　者：夏业茂[1] 勾建伟 

机构地区：[1]南京林业大学理学院应用数学系,南京210037

出　　处：《应用数学学报》2015年第4期751-768,共18页Acta Mathematicae Applicatae Sinica

基　　金：国家自然科学基金(11471161);南京林业大学高学历人才项目(163101004);南京市留学回国人员科技择优资助项目(013101001)资助

摘　　要：数据的异质性因相关的解释变量被排除在既定模型.然而,目前经典统计方法难以处理的异质参数的依赖关系或"结".为了解决非均质参数之间的依赖关系,本文基于多水平因子分析模型提出一个半参数贝叶斯分析程序.对于模型的截距和/或协方差结构参数的分布赋予折断的Dirichlet过程先验.在贝叶斯马尔可夫链蒙特卡罗框架内,分块Gibbs抽样器被用来执行后验分析.统计推断的基础上进行这些观察的经验分布.仿真研究表明,忽略了非均质参数之间的联系会导致不变参数估计产生严重的偏差.Heterogeneity among the observed data arises when the relevant explanatory variables are excluded from the posited model. However, current classic statistical method is difficult to deal with the dependence or ties among the heterogeneous parameters. To address this problem, in this paper, we developed a semiparametric Bayesian procedure for multilevel factor analysis model. A truncated Dirichlet process prior is used to model the distributions of the intercept and/or covariance structural parameters. Within the Bayesian Makov chains Monte Carlo framework, blocked Gibbs sampler is implemented to draw observations from the complicated posterior. Statistical inferences are carried out based on the empirical distribution of these observations. A simulation study shows that ignoring ties among the heterogeneous parameters will lead to serious biases for subject-invariant parameters.

关 键 词：多水平因子分析模型 MCMC算法 分块Gibbs抽样器 折断Dirichlet过程先验 

分 类 号：O212.8[理学—概率论与数理统计] O212.4[理学—数学]