本文選題：項目反應理論(IRT) + Copula理論　； 參考：《沈陽師范大學》2017年碩士論文

【摘要】：項目反應理論(IRT)作為一種現(xiàn)代教育和心理測量方法,在實際測量中的應用越來越廣泛。通常我們在利用項目反應模型處理問題時,為了方便,總是假設給定同一被試的情況下,項目反應是獨立且無關聯(lián)的,但這與很多實際測驗背景并不符合,影響了測量的準確性和可信度。有效地處理局部殘差相依問題是項目反應模型得以應用的前提。隨著現(xiàn)代統(tǒng)計學及數(shù)學的發(fā)展,處理局部相依問題的方法也在不斷發(fā)展。常見的處理方法是額外添加隨機效應因子,比如有學者提出了用題組項目反應模型。但是該方法建立的聯(lián)合反應分布函數(shù),會存在一些問題,例如邊際分布的不可復制性,導致原有項目反應模型中的一些參數(shù),比如題目難度參數(shù)、區(qū)分度參數(shù)失去具體意義,難以解釋。本文主要借助Copula函數(shù)來解決項目反應理論中局部殘差的問題。Copula函數(shù)作為一個新興的連接函數(shù),在金融領域中被廣泛應用。針對多個邊際反應分布建立模型,求出它們的聯(lián)合分布,同時考慮各個邊際分布間的相關性,解決了邊際分布不可復制性及參數(shù)解釋問題。對應建立起來的Copula函數(shù)就是各個邊際的聯(lián)合分布函數(shù)。在此基礎上,通過MCMC估計方法,給出項目反應模型中的項目參數(shù)及Copula連接函數(shù)中相關系數(shù)的貝葉斯后驗估計。主要利用統(tǒng)計軟件R來模擬和分析數(shù)據(jù),由Copula模型生成數(shù)據(jù),然后調(diào)用R2WinBUGS軟件包來得出模型的后驗估計結(jié)果,相關程序代碼見附錄。通過選取Frank copula函數(shù)和Clayton copula函數(shù),分析實際相依反應數(shù)據(jù),得出結(jié)論,當忽略數(shù)據(jù)的相依性,假設項目反應理論的局部獨立性建模時,帶來的估計偏差比較大,這對選題及被試能力評估都會有較大的影響。
[Abstract]:The project response theory (IRT), as a modern educational and psychological measurement method, is becoming more and more widely used in actual measurement. Usually, when we use the project response model to deal with the problem, we always assume that the project reaction is independent and unrelated under the assumption that the same test is given, but this is not with many actual test background. It affects the accuracy and reliability of the measurement. It is the premise for the application of the project response model to deal with the local residual dependence effectively. With the development of modern statistics and mathematics, the methods to deal with the local dependent problems are also developing. The common treatment method is to add random effect factors, such as a scholar. There are some problems in the joint reaction distribution function established by this method, such as the non reproducibility of the marginal distribution, which leads to some parameters in the original project reaction model, such as the parameter of the title difficulty, the distinction parameter loses its specific meaning, which is difficult to explain. This paper mainly uses the Copula function to solve the problem. The.Copula function of the problem of partial residual in the theory of project response is widely used in the financial field as a new connection function. A model is established for multiple marginal reaction distribution, and their joint distribution is obtained. At the same time, the correlation between the marginal distributions is considered, and the problem of non reproducible distribution of marginal distribution and the problem of parameter interpretation are solved. The corresponding Copula function is the joint distribution function of each marginal. On this basis, the project parameters in the project response model and the Bayesian posterior estimation of the correlation coefficient in the Copula connection function are given by the MCMC estimation method. The data are simulated and analyzed by the statistical software R, and the data are generated from the Copula model, and then the data are generated by the Copula model. The R2WinBUGS software package is called to get the results of the posterior estimation of the model, and the related program code is shown in the appendix. By selecting the Frank copula function and the Clayton copula function, the actual dependent response data are analyzed, and the conclusion is drawn. When the dependency of the data is ignored, the estimation deviation is larger when the Bureau independence of the project reaction theory is modeled. This will have a greater impact on the topic selection and the ability assessment of the subjects.
【學位授予單位】：沈陽師范大學
【學位級別】：碩士
【學位授予年份】：2017
【分類號】：F224

【參考文獻】

相關期刊論文 前10條

1 付志慧;李斌;;多維二參數(shù)Logistic項目反應模型的Gibbs抽樣法[J];沈陽師范大學學報(自然科學版);2014年03期

2 鐘波;張鵬;;Copula選擇方法[J];重慶工學院學報(自然科學版);2009年05期

3 曾莉;辛濤;張淑梅;;2PL模型的兩種馬爾可夫蒙特卡洛缺失數(shù)據(jù)處理方法比較[J];心理學報;2009年03期

4 于波;陳希鎮(zhèn);杜江;;Copula函數(shù)的選擇：方法與應用[J];數(shù)理統(tǒng)計與管理;2008年06期

5 劉樂平;張美英;李姣嬌;;基于WinBUGS軟件的貝葉斯計量經(jīng)濟學[J];東華理工學院學報(社會科學版);2007年02期

6 王沁;;生成Copula的兩種簡單方法[J];浙江大學學報(理學版);2006年02期

7 單國莉,陳東峰;一種確定最優(yōu)Copula的方法及應用[J];山東大學學報(理學版);2005年04期

8 辛濤;;項目反應理論研究的新進展[J];中國考試;2005年07期

9 馬躍淵,徐勇勇;Gibbs抽樣算法及軟件設計的初步研究[J];計算機應用與軟件;2005年02期

10 羅芬,丁樹良,胡小松,萬宇文,甘登文;基于IRT若干參數(shù)估計方式的比較[J];江西師范大學學報(自然科學版);2003年01期

相關博士學位論文 前2條

1 李榮;基于MCMC的貝葉斯Copula模型構(gòu)建及應用研究[D];湖南大學;2014年

2 付志慧;多維項目反應模型的參數(shù)估計[D];吉林大學;2010年

相關碩士學位論文 前2條

1 劉洋;基于MCMC的協(xié)整分析研究及其應用[D];武漢理工大學;2008年

2 韓艷敏;NOMMLE分布的參數(shù)估計與MCMC模擬研究[D];武漢理工大學;2007年

，

本文編號：2092428