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研究生： 郭柏甫
Po-Fu Kuo
論文名稱： Q矩陣錯誤設定在G-DINA模型下對參數估計和辨識率之影響
The Effects of Q-matrix Misspecification on Parameter Estimates and Classification Accuracy of the Generalized DINA Model
指導教授： 蔡蓉青
Tsai, Rung-Ching
學位類別： 碩士
Master
系所名稱： 數學系
Department of Mathematics
論文出版年： 2013
畢業學年度： 101
語文別： 英文
論文頁數： 44
中文關鍵詞： Q矩陣錯誤設定 、G-DINA模型 、辨識率
英文關鍵詞： Q-matrix misspecification, G-DINA model, Classification accuracy
論文種類： 學術論文
相關次數： 點閱：334  下載：22 
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    • 本篇研究探討Q矩陣的過度設定與不足設定對G-DINA模型參數估計和分類辨識率造成的影響，並使用平均絕對誤差(MAD)及個別概念辨識率、認知組型辨識率做為評估指標。研究結果發現Q矩陣不足設定對模型參數估計、辨識率及一些特定認知組型的正確答題機率造成影響，反之Q矩陣過度設定在各方面皆影響不大。此外一些因子如樣本數及認知組型的分佈在Q矩陣不足設定時也會造成影響。

    This study investigates the influence of different types of Q-matrix misspecification on parameter estimates and classification accuracy of the G-DINA model. In particular, underspecification and overspecification are the two types of Q-matrix misspecification
    under consideration. Furthermore, mean absolute deviation and classification accuracy index are used as the indices for parameter estimates and classification accuracy, respectively. Our results show that underspecification has a great impact on item parameter estimates, as well as on the probability of answering an item correctly for some latent mastery patterns. In contrast, overspecification has little impact on parameter estimates.
    Classification accuracy is also influenced by underspecification,with interactions with sample sizes as well as the distribution of underlying cognitive attribute patterns.

    1 Introduction-------------------------6 2 Method-------------------------------9 2.1 The G-DINA Model-----------------9 2.2 Estimation----------------------10 2.3 Evaluation Indices--------------12 3 Simulation--------------------------15 3.1 Data generation-----------------15 3.1.1 The Q-matrix------------------15 3.1.2 Parameter Values--------------16 3.2 Manipulated factors-------------18 3.2.1 Sample size-------------------18 3.2.2 Distribution of the attribute patterns--18 3.3 Condition settings--------------21 3.3.1 Underspeci cation-------------21 3.3.2 Overspeci cation--------------22 4 Results-----------------------------23 4.1 E ect on parameter estimates----23 4.2 E ect on classi cation accuracy-36 4.2.1 Effect on the attribute-speci c classi cation accuracy----------------------36 4.2.2 E ect on the overall classi cation accuracy--38 5 Summary and Conclusion--------------41 6 Reference---------------------------42

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