臺灣博碩士論文加值系統

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 Underspecication-------------21
3.3.2 Overspecication--------------22
4 Results-----------------------------23
4.1 Eect on parameter estimates----23
4.2 Eect on classication accuracy-36
4.2.1 Effect on the attribute-specic classication
accuracy----------------------36
4.2.2 Eect on the overall classication accuracy--38
5 Summary and Conclusion--------------41
6 Reference---------------------------42

Chang, H, H., Cui, Y., &; Gierl, J, M. (2012). Estimating classication consistency and accuracy for cognitive diagnostic assessment. Journal of Educational Measurement, 49,19-38.
Choi, H, J., Templin, J., Cohen, A., &; Atwood, C. (2010). The impact of model misspecication on estimation accuracy in diagnostic classication models. Paper pre-sented at the annual meeting of the National Council on Measurement in Education in Denver, Colorado.
Corter, J. E. &; Im, S. (2011). Statistical consequences of attribute misspecication in the rule space method. Educational and Psychological Measurement, 71(4), 712-731.
de la Torre, J. (2011). The generalized DINA model framework. Psychometrika, 76(2),179-199.
de la Torre, J., Deng, W., &; Hong, Y. (2010). Factors aecting the item parameter estimation and classication accuracy of the DINA model. Journal of Educational Measurement, 47(2), 227-249.
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. (2008). An empirically based method of Q-matrix validation for the DINA model: Development and applications .Journal of Educational Measurement, 45(4), 343-362.
de la Torre, J. &; Douglas, J. (2004). Higher-order latent trait models for cognitive diagnosis. Psychometrika, 69(3), 333-353.
DeCarlo, T, L. (2012). Recognizing Uncertainty in the Q-Matrix via a Bayesian Ex-tension of the DINA Model. Applied Psychological Measurement, 36(6), 447-468.
DeCarlo, T, L. (2011). On the analysis of fraction subtraction data: The DINA model classication latent class sizes, and the Q-Matrix. Applied Psychological Measurement, 35(1), 8-26.
DiBello, L. V., Roussos, L. A., &; Stout, W.F. (2007). Review of cognitively diagnostic assessment and a summary of psychometric models. In C. R. Rao and S. Sinharay (Eds.), Handbook of Statistics, 26 (pp. 979-1030). Amsterdam: Elsevier.
Hong, C, Y. (2013). Estimation of Generalized DINA Model with Order Restrictions. master thesis. Taiwan, Taipei: National Taiwan Normal University.
Henson, R. A., Templin, J. L., &; Willse, J. T. (2009). Dening a family of cognitive diagnosis models using log-linear models with latent variables. Psychometrika, 74(2), 191-210.
Junker, B. W., &; Sijtsma, K. (2001). Cognitive assessment models with few assump-tions, and connections with nonparametric item response theory. Applied Psychological Measurement, 25, 258-272.
Kunina-Habenicht, O., Rupp, A, A., &; Wilhelm, O. (2012). The impact of model mis-specication on parameter estimation and item-t assessment in log linear diagnostic classication models. Journal of Educational Measurement, 49, 59-81.
Maris,E. (1999). Estimating multiple classication latent class models. Psychometrika, 64, 187-212.
Rupp, A, A., &; Templin, J. (2008). The Eects of Q-Matrix misspecication on parameter estimates and classication accuracy in the DINA Model. Educational andPsychological Measurement, 68, 76-96.
Tatsuoka, K. K. (1983). Rule-space: An approach for dealing with misconceptions based on item response theory. Journal of Educational Measurement, 20, 345-354.
von Davier, M. (2010). Hierarchical mixtures of diagnostic models. Psychological Test and Assessment Modeling, 52(1), 8-28.
von Davier, M. (2005). A general diagnostic model applied to language testing data.(ETS Research Report RR-05-16).
Wang, W, C. (2010). Compare the Parameters Estimated by DINA Model with by G-DINA Model. master thesis. Taiwan, Taichung: National Taichung University of Education.