本文關(guān)鍵詞：IRT框架下的不可忽略缺失過程建模及Bayes估計研究　出處：《沈陽師范大學(xué)》2015年碩士論文　論文類型：學(xué)位論文

  更多相關(guān)文章： 項目反應(yīng)理論(IRT) Gibbs抽樣 不可忽略缺失數(shù)據(jù)

【摘要】：項目反應(yīng)理論(IRT)是克服了經(jīng)典測驗理論(CTT)的局限,在潛在特質(zhì)理論基礎(chǔ)上發(fā)展起來的,主要是探討被試在測驗項目上的反應(yīng)與被試潛在特質(zhì)之間的關(guān)系,因此項目反應(yīng)理論的核心問題是參數(shù)估計問題。參數(shù)估計過程中,常常要求數(shù)據(jù)完整,對于缺失數(shù)據(jù)的項目參數(shù)估計引起了國內(nèi)外廣大學(xué)者的重視。由于不可忽略缺失的廣泛存在,缺失數(shù)據(jù)的處理方法是項目反應(yīng)理論的一個研究熱點(diǎn)。本文主要研究教育與心理測量中的不可忽略缺失數(shù)據(jù)的建模和估計問題。利用項目反應(yīng)模型來擬合缺失指標(biāo),對觀測數(shù)據(jù)和缺失數(shù)據(jù)聯(lián)合建模,基于數(shù)據(jù)擴(kuò)充技術(shù)的Gibbs抽樣方法,同時給出對觀測數(shù)據(jù)模型和缺失指標(biāo)模型的后驗估計。第一章對項目反應(yīng)理論的發(fā)展,當(dāng)前國內(nèi)外的研究現(xiàn)狀及本篇論文的主要工作進(jìn)行了簡要的介紹;第二章介紹了相對于經(jīng)典測驗理論項目反應(yīng)理論的優(yōu)勢,本文采用的項目反應(yīng)模型,MCMC估計方法以及一些基本概念、基本理論。第三章研究了二級評分模型下不可忽略缺失數(shù)據(jù)的Bayes估計問題,采用二級評分模型來擬合觀測數(shù)據(jù),用Rasch擬合缺失指標(biāo),對觀測數(shù)據(jù)和缺失數(shù)據(jù)的聯(lián)合建模,進(jìn)而采用Gibbs抽樣方法,給出對觀測數(shù)據(jù)模型和缺失指標(biāo)模型的后驗估計。第四章研究了等級評分模型下不可忽略缺失數(shù)據(jù)的Bayes估計問題,用等級評分模型擬合觀測數(shù)據(jù),Rasch擬合缺失指標(biāo),通過聯(lián)合建模,利用Gibbs估計方法對模型進(jìn)行參數(shù)估計。每章均通過模擬研究驗證了所用方法有效的減小了由于忽略缺失數(shù)據(jù)估計參數(shù)時產(chǎn)生的偏差,論文最后給出了階段性總結(jié),提出未來的研究方向和工作設(shè)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.

【學(xué)位授予單位】：沈陽師范大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2015
【分類號】：C81

【相似文獻(xiàn)】

相關(guān)期刊論文 前10條

1 金勇進(jìn);缺失數(shù)據(jù)的加權(quán)調(diào)整(系列之Ⅳ)[J];數(shù)理統(tǒng)計與管理;2001年05期

2 楊金英;崔朝杰;;圖模型方法用于二值變量相關(guān)性分析中缺失數(shù)據(jù)的估計[J];中國衛(wèi)生統(tǒng)計;2012年05期

3 金勇進(jìn);缺失數(shù)據(jù)的偏差校正(系列三)[J];數(shù)理統(tǒng)計與管理;2001年04期

4 張朝雄;沈e，

本文編號：1384068