臺灣博碩士論文加值系統

現今教改訴求的是─「把每一位學生帶上來」。但先決條件，就是要知道每個學生的長處與短處，才可以設計策略，實施補救教學。而一般傳統測驗，僅提供學生在團體中的量尺分數，並無法顯現出學生是否精熟某種技能的訊息，進而幫助學生或老師更加瞭解分數所代表的涵意，進行更有效率的學習。認知診斷模型可以提供解決的方案，而認知診斷模型中以DINA模式最簡單也最容易解釋，並已有許多學者投入模式開發、實際應用的研究。
本研究透過模擬研究方式探討Q矩陣設計在不同試題參數、不同概念數、不同樣本數下，分別以DINA模型及G-DINA模型估計的成效差異。
研究結果顯示：
一、 不平衡的Q矩陣設計估計準確性較平衡的Q矩陣為佳。
二、 較大的樣本數能提高DINA、G-DINA模式估計的準確性。
三、 試題參數值設定較小時，估計準確性高。
四、 題數相同時，概念數較少時估計的準確性佳於概念數多。
五、 在概念數相同時，測驗長度較長時的估計準確性較好。
六、 模擬資料以DINA模式估計較以G-DINA模式估計準確。
七、 以DINA模式及G-DINA模式分析實徵資料，結果與本研究相符。

Demands of today's education reform is ─ "No Child Left Behind." But the prerequisite is to know the strengths and weaknesses of each student. Then we can design the remedial program. The traditional test only shows the students’ scale score in the groups, but can’t show the message of whether a student mastery a skill, and can’t help the students or the teachers a better understanding of the meaning represented by scores, and make more efficient learning. The cognitive diagnosis models can provide a solution. In the cognitive diagnostic models, DINA model is the simplest and easiest to explain. Many scholars have been involved in the application of research, model development, etc.
This study simulate the Q matrix with different design on variety parameters in items, amounts of attributes , sample sizes, respectively. And uses DINA and G-DINA model to estimate the effectiveness of the differences.
The results showed:
1. When Q matrix is unbalance, the accuracy of estimation is better.
2. When sample’s size increased, it may improve the accuracy of estimation.
3. When the item’s parameter value is smaller, the accuracy of estimation is higher.
4. When amount of items is the same, the amount of attributes is larger, the accuracy
of estimation is better.
5. When the amount of attributes is the same, the test’s length is larger, the accuracy of
estimation is better.
6. Simulated data estimated by DINA model is better than G-DINA model.
7. The empirical data estimated by DINA model and G-DINA model has the same results with this study.

摘要 ………………………………………………………………………………I.
目錄……………………………………………………………………………….III
表目錄……………………………………………………………………………IV
圖目錄……………………………………………………………………………VI
第一章 研究動機與目的 …………………………………………………………1
第一節 研究動機 …………………………………………………………1
第二節 研究目的 …………………………………………………………4
第三節 名詞解釋 …………………………………………………………5
第二章 文獻探討……………………………………………………………………6
第一節 認知診斷評量模型……………………………………………………6
第二節 參數估計法……………………………………………………………15
第三章 研究方法……………………………………………………………………20
第一節 研究設計………………………………………………………………20
第二節 評估指標………………………………………………………………31
第三節 研究工具………………………………………………………………32
第四章 研究結果……………………………………………………………………35
第一節 實驗結果………………………………………………………………35
第二節 綜合比較………………………………………………………………47
第三節 實徵資料驗證…………………………………………………………51
第五章結論與建議…………………………………………………………………54
第一節 結論……………………………………………………………………54
第二節 建議……………………………………………………………………57
參考文獻……………………………………………………………………………58

甘媛源與余嘉元(2009)。心理測量理論的新進展：潛在分類模型。中國考試，2009(3)，3-8。
余民寧(2009)。試題反應理論(IRT)及其應用。臺北市：心理出版社。
涂金堂(2003)。認知診斷評量的探究。臺南師範學院學報，37(2):67-97。
洪祥堯(2009)。資訊科技融入國小六年級圓形圖單元教學與評量之行動研究。亞
洲大學資訊工程學系碩士論文，未出版，臺中縣。

英文部份
Bock, R. D. & Aitkin, M. (1981) Marginal maximum likelihood estimation of item parameters：Application of an EM algorithm. Psychometrika, 46, 443-459.
Cheng, Y., & Chang, H. (2009). When cognitive diagnosis meets computerized adaptive testing: CD-CAT. Psychometrika, 74(4), 619–632.
de la Torre, J., & Douglas, J. (2004). Higher-order latent trait models for cognitive diagnosis. Psychometrika. 69(3),333-353.
de la Torre, J., & Douglas, J. (2008). Model evaluation and multiple strategies in cognitive diagnosis: An analysis of fraction subtraction data. Psychometrika,73(4), 595-624.
de la Torre, J., & Liu, Y. (2008, March). A cognitive diagnosis model for continuous response. Paper presented at the meeting of the National Council on Measurement in Education, New York, NY.
de la Torre, J. (2009a). DINA model and parameter estimation: A didactic. Journal of Educational and Behavioral Statistics, 34, 115-130.
de la Torre, J. (2009b). A cognitive diagnosis model for cognitively-based multiple-choice options. Applied Psychological Measurement, 33, 163-183.

de la Torre, J.,& Lee (2010). A note on the invariance of DINA model parameters. Journal of Measurements, 47, 115-127.
Doornik, J. A. (2003). Object-oriented matrix programming using Ox (Version 3.1). [Computer software]. London, England: Timberlake Consultants Press.
Doignon, J.P., & Falmagne, J.C. (1999). Knowledge spaces. New York: Springer.
Educational Testing Service (2004). Arpeggio: Release 1.1[Computer software]. Princeton, NJ: Author.
Fischer, G. H. (1973). The linear logistic test model as an instrument in educational research. Acta Psychologica, 37,59-374.
Finkelman, M., Kim, W., & Roussos, L. (2009). Automated test assembly for cognitive diagnostic models using a genetic algorithm. Journal of Educational Measurement, 46 (3), 273-292.
Geman, S., & Geman, D. (1984). Stochastic relaxation, Gibbs distributions, and the
Bayesian restoration of images. IEEE Transcationa on Pattern Analysis and
Machine Intelligence, 6, 721-741.
Gierl, M., Cui, Y., & Zhou, J. (2009). Reliability and attribute-based scoring in cognitive diagnostic assessment. Journal of Educational Measurement, 46 (3), 293-313.
Henson, R. A., & Douglas, J. (2005). Test construction for cognitive diagnosis. Applied Psychological Measurement, 29 (4), 262-277.
Hartz, S. (2002). A Bayesian framework for the Unified Model for assessing cognitive abilities: blending theory with practice. Unpublished doctoral thesis, University of Illinois at Urbana-Champain.
Henson, R., Templin J., & Willse, J. (2009). Defining a family of cognitive diagnosis models using log-linear models with latent variables. Psychometrika, 74(2), 191-210.
Huebner, (2010).Cognitive Diagnostic Computer Adaptive Assessments . Journal of Educational Measurement, 46 (3),293-313.


Huebner, Alan, (2010). An Overview of Recent Developments in Cognitive Diagnostic Computer Adaptive Assessments. Practical Assessment, Research & Evaluation, 15(3), January 2010, form http://pareonline.net/getvn.asp?v=15 &n=3.
Junker, B., & Sijtsma, K. (2001). Cognitive assessment models with few assumptions, and connections with nonparametric item response theory. Applied Psychological Measurement, 25(3), 258-272.
Leighton, J. P., Gierl, M. J., & Hunka, S. M. (2004). The attribute hierarchy method for cognitive assessment: a variation on Tatsuoka’s rule space approach. Journal of Educational Measurement, 41(3), 205–237.
Maris, E. (1999). Estimating multiple classification latent class models. Psychometrika, 64(2), 187-212.
McGlohen, M., & Chang, H. (2008). Combining computer adaptive testing technology with cognitively diagnostic assessment. Behavior Research Methods, 40 (3), 808-821.
Muthén, L.K., & Muthén, B.O. (1998-2006). M-plus user’s guide(4th ed.). Los Angeles: Muthén, L.K., & Muthén.
Patz, R. J., & Junker, B. W. (1999). A straightforward approach to Markov Chain
Monte Carlo methods for item response models. Journal of Educational and
Behavioral Statistics, 24(2), 146-178.
Rupp, A., & Templin, J. (2008). The effects of q-matrix misspecification on parameter Estimates and classification accuracy in the DINA model. Educational and Psychological Measurement, 68(1), 78-96.
Sheehan, K, M.(1997). A tree-based approach to proficiency scaling and diagnostic assessment . Journal of Educational Measurement, 34, 333-352.
Tatsuoka, K. K. (1983). Rule space: An approach for dealing with misconception based on item response theory. Journal of Educational Measurement, 20, 345-354.
Tatsuoka, K. K. (1985).A probabilistic model for diagnosing misconceptions by the pattern classification approach. Journal of Educational Statistics, 10, 55-73.

Templin, J. L., Henson, R. A., L. (2006). Measurement of psychological disorders using cognitive diagnosis models. Psychological Methods, 11(3), 287–305
Templin, J. L., Henson, R. A., Templin, S. E., & Roussos, L. (2008). Robustness of Hierarchical Modeling of Skill Association in Cognitive Diagnosis Models. Applied Psychological Measurement, 32(7), 559–574.
Tierney, L. (1994). Exploring posterior distributions with Markov Chains. Annals of
Statistics, 22, 1701-1762.
von Davier, M. (2005). A General diagnostic model applied to language testing data. ETS Research Report. Princeton, New Jersey: ETS.
Xu, X., Chang, H., & Douglas, J. (2003). A simulation study to compare CAT strategies for cognitive diagnosis. Paper presented at the annual meeting of the American Educational Research Association, Chicago.
Xu, X. & von Davier, M. (2008). Linking for the general diagnostic model. ETS Research Report. Princeton, New Jersey: ETS.