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研究生: 賴韻婷
Lai, Yun-Ting
論文名稱: The Effects of Incomplete Q-Matrix on Parameter Estimates and Classification Accuracy in the DINA and DINO Models and Non-parametric Approach
The Effects of Incomplete Q-Matrix on Parameter Estimates and Classification Accuracy in the DINA and DINO Models and Non-parametric Approach
指導教授: 蔡碧紋
Tsai, Pi-Wen
學位類別: 碩士
Master
系所名稱: 數學系
Department of Mathematics
論文出版年: 2018
畢業學年度: 106
語文別: 英文
論文頁數: 69
中文關鍵詞: 認知診斷不完備的Q矩陣DINADINO無母數方法等價分類
英文關鍵詞: Cognitive Diagnosis, Incomplete Q-matrix, DINA, DINO, Non-parametric Classification, Equivalence Class
DOI URL: http://doi.org/10.6345/THE.NTNU.DM.016.2018.B01
論文種類: 學術論文
相關次數: 點閱:125下載:0
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  • 用Q矩陣為基礎以側寫考生認知的認知診斷模型越來越受關注,故確保認知辨識性的Q矩陣完備性很重要。然而,要準備一份具有Q矩陣完備性的測驗往往是很困難的,尤其是當感興趣的能力數量很大時。因此,本文主要的目的是探究不完備Q矩陣對認知辨識率的準確度和認知診斷模型的參數估計的影響。我們探究了不完備Q矩陣對DINA/DINO模型和無母數方法的影響。透過模擬研究不同設定下不完備Q矩陣的影響。在這三個模型的認知辨識率上使用等價分類的概念探究不完備Q矩陣的影響。模擬結果顯示,不完備Q矩陣的影響並不如我們預期的嚴重,特別是在即使有完備Q矩陣亦無法準確分類的狀況。在認知辨識率的比較,參數模型在面對不完備Q矩陣時更具穩健性。且不完備的Q矩陣對參數模型的題目參數估計沒有顯著影響。

    There has been growing interest in Q-matrix based cognitive diagnosis models to assess examinees’ attribute profiles. The completeness of Q-matrix is important for assuring the identification of all attribute profile classes. However, it is often difficult to have assessments with complete Q-matrix especially when the number of attributes of interest is large. The main objective of this research it to study the effects of incomplete Q-matrix on the classification accuracy of examinees’ attribute profiles and on the parameter estimates for the cognitive diagnosis models. We investigate the effects of incomplete Q-matrix in the DINA/DINO models and the non-parametric method suggested by Chiu & Douglas (2013). Simulation studies are carried out to study the effects of incomplete Q-matrix under different scenarios. The idea of the equivalence class is used on the classification accuracy for these three models to explore the effect of incomplete Q-matrix. Our results show that the effects of incomplete Q-matrix were not as formidable as we expected, especially for the cases where the imprecise classification will happen even with complete Q-matrix. As for the classification accuracy, the parametric model is more robust than the non-parametric approach. Moreover, incomplete Q-matrix did not have a significant effect on the maximum likelihood estimation of item parameters.

    1 Introduction 1 2 Cognitive Diagnosis Models and Non-parametric Approach 7 2.1 The Deterministic Input Noisy Output “AND” Gate Model 8 2.2 The Deterministic Input Noisy Output “OR” Gate Model 11 2.3 Non-parametric Approach 12 3 Q-Completeness and Equivalence Class 15 4 Simulation Study 19 4.1 Simulation Design 20 4.1.1 Sample Size 20 4.1.2 Test Length 20 4.1.3 Number of Attributes 21 4.1.4 Number of Missing Single Attributes 21 4.1.5 Examinees Traits 21 4.1.6 Item Parameters 22 4.1.7 Q-matrix 27 4.1.8 Agreement Rate 27 4.2 Results 28 5 Discussions 63 6 Conclusions 65 References 67

    Cheng, Y. (2009). When cognitive diagnosis meets computerized adaptive testing: Cd-cat. Psychometrika, 74(4), 619.
    Chiu, C.-Y., & Douglas, J. (2013). A nonparametric approach to cognitive diagnosis by proximity to ideal response patterns. Journal of Classification, 30(2), 225–250.
    Chiu, C.-Y., Douglas, J. A., & Li, X. (2009). Cluster analysis for cognitive diagnosis: Theory and applications. Psychometrika, 74(4), 633–665.
    Chung, M., & Johnson, M. S. (2018). An mcmc algorithm for estimating the q-matrix in a bayesian framework. arXiv preprint arXiv:1802.02286 .
    Davier, M. (2005). A general diagnostic model applied to language testing data. ETS Research Report Series, 2005(2).
    de la Torre, J. (2009). Dina model and parameter estimation: A didactic. Journal of educational and behavioral statistics, 34(1), 115–130.
    de la Torre, J. (2011). The generalized dina model framework. Psychometrika, 76(2), 179–199.
    de la Torre, J., & Douglas, J. A. (2004). Higher-order latent trait models for cognitive diagnosis. Psychometrika, 69(3), 333–353.
    DiBello, L. V., Stout, W. F., & Roussos, L. A. (1995). Unified cognitive/psychometric diagnostic assessment likelihood-based classification techniques. Cognitively diagnostic assessment, 361–389.
    Henson, R. A., Templin, J. L., & Willse, J. T. (2009). Defining a family of cognitive diagnosis models using log-linear models with latent variables. Psychometrika, 74(2), 191.
Junker, B. W., & Sijtsma, K. (2001). Cognitive assessment models with few assumptions, and connections with nonparametric item response theory. Applied Psychological Measurement, 25(3), 258–272.
Kohn, H.-F., & Chiu, C.-Y. (2016a). Conditions of completeness of the q-matrix of tests for cognitive diagnosis. In Quantitative psychology research (pp. 255–264). Springer.
Kohn, H.-F., & Chiu, C.-Y. (2016b). A proof of the duality of the dina model and the dino model. Journal of Classification, 33(2), 171–184.
Kohn, H.-F., & Chiu, C.-Y. (2017). A procedure for assessing the completeness of the q-matrices of cognitively diagnostic tests. Psychometrika, 82(1), 112–132.
Liu, J., Xu, G., & Ying, Z. (2011). Learning item-attribute relationship in q-matrix based diagnostic classification models. arXiv preprint arXiv:1106.0721.
Liu, J., Xu, G., & Ying, Z. (2012). Data-driven learning of q-matrix. Applied psychological measurement, 36(7), 548–564.
Liu, J., Xu, G., & Ying, Z. (2013). Theory of the self-learning q-matrix. Bernoulli: official journal of the Bernoulli Society for Mathematical Statistics and Probability, 19(5A), 1790.
Maris, E. (1999). Estimating multiple classification latent class models. Psychometrika, 64(2), 187–212.
Robitzsch, A., Kiefer, T., George, A., & Uenlue, A. (2014). Cdm: Cognitive diagnosis modeling. r package version 3.1-14. Retrieved from the Comprehensive R Archive Network [CRAN] website http://CRAN. R-project. org/package= CDM.
    Tatsuoka, K. K. (1985). A probabilistic model for diagnosing misconceptions by the pattern classification approach. Journal of Educational Statistics, 10(1), 55–73.
    Tatsuoka, K. K. (1991). Boolean algebra applied to determination of universal set of knowledge states. ETS Research Report Series, 1991(2).
Templin, J. L., & Henson, R. A. (2006). Measurement of psychological disorders using cognitive diagnosis models. Psychological methods, 11(3), 287.

    Zhang, S. S., DeCarlo, L. T., & Ying, Z. (2013). Non-identifiability, equivalence classes, and attribute-specific classification in q-matrix based cognitive diagnosis models. arXiv preprint arXiv:1303.0426.

    Zheng, Y., Chiu, C., & Douglas, J. (2014). Npcd: Nonparametric methods for cognitive diagnosis. r package version 1.0-5. Retrieved from the Comprehensive R Archive Network [CRAN] website http://CRAN. R-project. org/package= NPCD.

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