本文選題：認(rèn)知診斷評(píng)估 + Q矩陣估計(jì)��； 參考：《華中師范大學(xué)》2017年碩士論文

【摘要】：認(rèn)知診斷以微觀認(rèn)知視角對(duì)學(xué)生的學(xué)習(xí)過(guò)程做出科學(xué)的準(zhǔn)確評(píng)估,已經(jīng)在心理學(xué)和教育數(shù)據(jù)挖掘領(lǐng)域中發(fā)揮了巨大潛力。然而目前應(yīng)用認(rèn)知診斷理論編制的測(cè)驗(yàn)有限,其主要困難是反映項(xiàng)目和屬性間關(guān)系的Q矩陣無(wú)法合理界定。構(gòu)建正確的Q矩陣是認(rèn)知診斷實(shí)踐中的關(guān)鍵環(huán)節(jié),是認(rèn)知診斷測(cè)驗(yàn)理論不同于傳統(tǒng)測(cè)量理論的本質(zhì)所在。Q矩陣的界定一般是由領(lǐng)域?qū)＜液托睦頊y(cè)量學(xué)家基于診斷目的,通過(guò)討論共同完成。但是這種方式存在著界定成本高、主觀性較強(qiáng)以及專(zhuān)家意見(jiàn)不一致等問(wèn)題。因此,認(rèn)知診斷亟需研究更加客觀地估計(jì)Q矩陣的方法,近年來(lái)這方面成為國(guó)內(nèi)外學(xué)者關(guān)注的焦點(diǎn),相繼研究出一系列的估計(jì)方法。本論文在研究了一些經(jīng)典Q矩陣估計(jì)方法的基礎(chǔ)上,主要針對(duì)經(jīng)典Barnes爬山法搜索能力差和易陷入局部極值的缺陷,提出利用全局優(yōu)化搜索的遺傳算法改進(jìn)經(jīng)典爬山法,實(shí)現(xiàn)Q矩陣的估計(jì),并提出借助DeCarlo貝葉斯法估計(jì)精度較高的優(yōu)勢(shì)對(duì)估計(jì)結(jié)果進(jìn)一步優(yōu)化。論文在模擬數(shù)據(jù)和真實(shí)數(shù)據(jù)集合上分別進(jìn)行了實(shí)驗(yàn)驗(yàn)證,通過(guò)分析Q矩陣邊際判準(zhǔn)率MMR、差異距離DD和模型擬合指數(shù)等評(píng)價(jià)指標(biāo)來(lái)研究新方法與其他方法估計(jì)性能的差異。模擬數(shù)據(jù)采用Xiang(2013)的方法生成,使用Monte Carlo模擬系統(tǒng)研究了測(cè)驗(yàn)學(xué)生人數(shù)、屬性數(shù)目和項(xiàng)目總數(shù)等因素對(duì)各方法估計(jì)性能的影響。真實(shí)數(shù)據(jù)來(lái)源于經(jīng)典的Tatsuoka分?jǐn)?shù)減法和SAT測(cè)驗(yàn),經(jīng)過(guò)實(shí)驗(yàn)對(duì)比驗(yàn)證了算法的實(shí)用性。大量實(shí)驗(yàn)研究表明:在同等條件下,本文遺傳算法的估計(jì)性能優(yōu)于Barnes爬山法和非線性懲罰估計(jì)法,而貝葉斯法進(jìn)一步優(yōu)化后的Q矩陣更加接近于真實(shí)Q矩陣,明顯提升了估計(jì)精度。
[Abstract]:Cognitive diagnosis has played a great potential in the field of psychology and educational data mining to make a scientific and accurate assessment of students' learning process from the perspective of micro-cognition. However, there are limited tests compiled by cognitive diagnostic theory, the main difficulty of which is that the Q matrix, which reflects the relationship between items and attributes, cannot be reasonably defined. Constructing a correct Q matrix is a key link in the practice of cognitive diagnosis. It is the essence of cognitive diagnostic test theory that is different from traditional measurement theory. The definition of Q matrix is generally based on the diagnostic purpose by domain experts and psychometrists. To complete together through discussion. But there are some problems in this way, such as high definition cost, strong subjectivity and different opinions of experts. Therefore, cognitive diagnosis needs to study the methods of estimating Q matrix more objectively. In recent years, researchers at home and abroad have paid close attention to this aspect, and a series of estimation methods have been developed one after another. In this paper, based on the study of some classical Q matrix estimation methods, the classical Barnes mountain climbing algorithm is proposed to improve the classical mountain climbing method by using the genetic algorithm with global optimization, which is poor in searching ability and easy to fall into local extremum. The estimation of Q matrix is realized, and the DeCarlo Bayesian method is proposed to further optimize the estimation results. In this paper, experiments are carried out on the set of simulation data and real data, and the performance difference between the new method and other methods is studied by analyzing the evaluation indexes such as the marginal accuracy rate of Q matrix MMRs, difference distance DD and model fitting index. The Monte Carlo simulation system was used to study the effects of the number of students, the number of attributes and the total number of items on the estimation performance of each method. The real data come from the classical Tatsuoka score subtraction and SAT test. A large number of experiments show that under the same conditions, the estimation performance of genetic algorithm in this paper is better than that of Barnes mountain climbing method and nonlinear penalty estimation method, and the Q matrix after further optimization by Bayesian method is closer to the real Q matrix. The estimation accuracy is obviously improved.
【學(xué)位授予單位】：華中師范大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2017
【分類(lèi)號(hào)】：B842.1;TP311.13

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