IRT框架下的不可忽略缺失过程建模及Bayes估计研究

发布时间：2018-01-05 17:15

本文关键词：IRT框架下的不可忽略缺失过程建模及Bayes估计研究　出处：《沈阳师范大学》2015年硕士论文　论文类型：学位论文

【摘要】：项目反应理论(IRT)是克服了经典测验理论(CTT)的局限,在潜在特质理论基础上发展起来的,主要是探讨被试在测验项目上的反应与被试潜在特质之间的关系,因此项目反应理论的核心问题是参数估计问题。参数估计过程中,常常要求数据完整,对于缺失数据的项目参数估计引起了国内外广大学者的重视。由于不可忽略缺失的广泛存在,缺失数据的处理方法是项目反应理论的一个研究热点。本文主要研究教育与心理测量中的不可忽略缺失数据的建模和估计问题。利用项目反应模型来拟合缺失指标,对观测数据和缺失数据联合建模,基于数据扩充技术的Gibbs抽样方法,同时给出对观测数据模型和缺失指标模型的后验估计。第一章对项目反应理论的发展,当前国内外的研究现状及本篇论文的主要工作进行了简要的介绍;第二章介绍了相对于经典测验理论项目反应理论的优势,本文采用的项目反应模型,MCMC估计方法以及一些基本概念、基本理论。第三章研究了二级评分模型下不可忽略缺失数据的Bayes估计问题,采用二级评分模型来拟合观测数据,用Rasch拟合缺失指标,对观测数据和缺失数据的联合建模,进而采用Gibbs抽样方法,给出对观测数据模型和缺失指标模型的后验估计。第四章研究了等级评分模型下不可忽略缺失数据的Bayes估计问题,用等级评分模型拟合观测数据,Rasch拟合缺失指标,通过联合建模,利用Gibbs估计方法对模型进行参数估计。每章均通过模拟研究验证了所用方法有效的减小了由于忽略缺失数据估计参数时产生的偏差,论文最后给出了阶段性总结,提出未来的研究方向和工作设想。
[Abstract]:Item response theory (IRT) is to overcome the classical test theory (CTT) limitations, developed in the latent trait theory basis, mainly discusses the subjects in the test item response test and the relationship between latent trait, so the core problem of item response theory is the problem of parameter estimation of the parameter estimation process. Often, data integrity requirements, for the estimation of missing data item parameters caused the majority of scholars at home and abroad. Because of the extensive attention should not be ignored in the absence of the missing data is a hot research project reaction theory. This paper focuses on the educational and psychological measurement should not be neglected in the modeling and estimation of missing data. Using item response model to fit the lack of indicators, to model data and missing data, Gibbs data sampling method based on extended technology, and given the number of observations According to the model and the lack of index model a posteriori estimation. In the first chapter, the development of item response theory, the main work of the current research status at home and abroad this thesis makes a brief introduction; the second chapter introduces the classic test theory, item response theory, this paper uses the item response model, the estimation method of MCMC and some of the basic concepts and basic theory. The third chapter studies the two scoring model can not be neglected when the Bayes missing data estimation, using two scoring model to fit the observed data, the use of Rasch fitting loss index, combined with modeling of the observed data and missing data, and then using Gibbs sampling method, the observation data and model the lack of index model gives a posteriori estimation. The fourth chapter studies the rating model can not be ignored Bayes missing data estimation problem, using grade model fitting observation According to Rasch, the lack of fit index, through joint modeling, estimation method of model parameter estimation using Gibbs. Each chapter was verified through simulation studies the proposed method effectively reduces the error due to ignoring missing data when estimating parameters, finally summarized, put forward the future research direction and work plan.

【学位授予单位】：沈阳师范大学
【学位级别】：硕士
【学位授予年份】：2015
【分类号】：C81

【相似文献】