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

【摘要】：項(xiàng)目反應(yīng)理論(IRT)作為一種現(xiàn)代教育和心理測量方法,在實(shí)際測量中的應(yīng)用越來越廣泛。通常我們在利用項(xiàng)目反應(yīng)模型處理問題時(shí),為了方便,總是假設(shè)給定同一被試的情況下,項(xiàng)目反應(yīng)是獨(dú)立且無關(guān)聯(lián)的,但這與很多實(shí)際測驗(yàn)背景并不符合,影響了測量的準(zhǔn)確性和可信度。有效地處理局部殘差相依問題是項(xiàng)目反應(yīng)模型得以應(yīng)用的前提。隨著現(xiàn)代統(tǒng)計(jì)學(xué)及數(shù)學(xué)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(jī)效應(yīng)因子,比如有學(xué)者提出了用題組項(xiàng)目反應(yīng)模型。但是該方法建立的聯(lián)合反應(yīng)分布函數(shù),會(huì)存在一些問題,例如邊際分布的不可復(fù)制性,導(dǎo)致原有項(xiàng)目反應(yīng)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(xiàng)目反應(yīng)理論中局部殘差的問題。Copula函數(shù)作為一個(gè)新興的連接函數(shù),在金融領(lǐng)域中被廣泛應(yīng)用。針對(duì)多個(gè)邊際反應(yīng)分布建立模型,求出它們的聯(lián)合分布,同時(shí)考慮各個(gè)邊際分布間的相關(guān)性,解決了邊際分布不可復(fù)制性及參數(shù)解釋問題。對(duì)應(yīng)建立起來的Copula函數(shù)就是各個(gè)邊際的聯(lián)合分布函數(shù)。在此基礎(chǔ)上,通過MCMC估計(jì)方法,給出項(xiàng)目反應(yīng)模型中的項(xiàng)目參數(shù)及Copula連接函數(shù)中相關(guān)系數(shù)的貝葉斯后驗(yàn)估計(jì)。主要利用統(tǒng)計(jì)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(yàn)估計(jì)結(jié)果,相關(guān)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(shí)際相依反應(yīng)數(shù)據(jù),得出結(jié)論,當(dāng)忽略數(shù)據(jù)的相依性,假設(shè)項(xiàng)目反應(yīng)理論的局部獨(dú)立性建模時(shí),帶來的估計(jì)偏差比較大,這對(duì)選題及被試能力評(píng)估都會(huì)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(xué)位授予單位】：沈陽師范大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2017
【分類號(hào)】：F224

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