臺灣博碩士論文加值系統

電腦適性化測驗的目的是藉由挑選難度與受測者能力相符的測驗試題來進行施測，進而達成專屬於受測者的個人化測驗內容。然而，對於擁有大量測驗試題的試題庫而言，電腦適性化測驗系統有兩大挑戰。其中一個挑戰為如何正確的估計測驗試題的試題難度指數；而另外一個挑戰是如何快速的挑選出最適合受測者能力水準的測驗試題。
本研究提出一個基於答題異常率的試題難度指數估計方法。受測者的能力值被直接考慮進估計的過程，也就是說，試題難度指數與受測者能力值可以被相互估計。每道測驗試題也可以獨立的進行估計。因此，試題庫可以隨時輕易地被擴充，且將可以在無需太多前測樣本的情況下，快速地估計出合理的試題難度指數。
本研究再以知識結構的概念作為受測者多重能力評估的準則，發展一個基於粒子群最佳化演算法的動態選題策略。由於粒子群最佳化演算法快速搜尋的優點與知識結構的特性，即使在擁有大量測驗試題的試題庫裡，也能快速的搜尋到最適合受測者能力水準的測驗試題。

The aim of computerized adaptive testing archives the personal test exclusively for a testee through selecting the test item with the difficulty, which is consistent with the current testee’s ability. However, for a big test item bank whit many test items, there are two important challenges to a computerized adaptive testing system. The first one is how to estimate the item difficulty indices of test items correctly; and the other one is how to locate a most suitable test item for a testee’s ability quickly.
An estimation method of item difficulty indices based on the answers abnormal rate is proposed in this study. The testees’ abilities are considered into the estimation process directly, in other words, the item difficulty indices and the testees’ abilities can be estimated mutually. Each test item can also be estimated independently. Therefore, the item bank can be expanded easily at any time, and the item difficulty indices will be estimated quickly and reasonably without too many pre-test samples.
And then, this study adopts the knowledge structure concept for multiple ability evaluation for testees, which is based on the particle swarm optimization, to develop a dynamic item selection strategy. The quick search advantage in the particle swarm optimization and knowledge structure characteristics allow the most suitable test items for a testee’s ability to be quickly identified, even in a big test item bank.

摘　　要 iv
ABSTRACT v
致　　謝 vi
目　　次 vii
表目錄 ix
圖目錄 x
第一章 緒論 1
1.1 研究動機 1
1.2 研究目的 3
1.3 論文架構 3
第二章 文獻探討 5
2.1 電腦適性化測驗 5
2.2 知識結構 6
2.3 試題分析 7
2.3.1 試題難度 7
2.3.2 試題鑑別度 8
2.4 試題反應理論 9
2.5 粒子群最佳化演算法 12
2.6 動態選題策略 15
2.7 Kappa一致性分析 17
第三章 研究方法 20
3.1 系統架構 20
3.2 試題難度調整策略 23
3.3 PSO動態選題策略 26
3.3.1 PSO的搜尋向量 26
3.3.1.1 試題難度控制因子 27
3.3.1.2 試題比例控制因子 27
3.3.1.3 試題曝光度控制因子 29
3.3.1.4 個人試題曝光度控制因子 29
3.3.1.5 搜尋向量 30
3.3.2 PSO的速度函數 31
3.3.3 PSO的適應函數 32
3.3.4 PSO適性化測驗 33
第四章 實驗與結果討論 35
4.1 實驗一：PSO動態選題策略之成效 35
4.1.1 搜尋準確度 36
4.1.2 搜尋速度 39
4.1.3 試題重疊率 42
4.2 實驗二：試題難度指數估計方法之成效 45
4.2.1 難度調整公式性能 45
4.2.2 出題次數影響難度調整調查 49
4.2.3 測驗結果一致性分析 50
第五章 結論與未來展望 52
參考文獻 53

[1]S.-C. Cheng, Y.-T. Lin, and Y.-M. Huang, “Dynamic question generation system for web-based testing using particle swarm optimization,” Expert Systems with Applications, Vol. 36, No. 1, pp. 616-624, 2009.
[2]Y.-M. Huang, Y.-T. Lin, and S.-C. Cheng, “An adaptive testing system for supporting versatile educational assessment,” Computers & Education, Vol. 52, No. 1, pp. 53-67, 2009.
[3]M. D. Anatchkova, R. N. Saris-Baglama, M. Kosinski, and J. B. Bjorner, “Development and Preliminary Testing of a Computerized Adaptive Assessment of Chronic Pain,” The Journal of Pain, Vol. 10, No. 9, pp. 932-943, 2009.
[4]E.-S. M. El-Alfy and R. E. Abdel-Aal, “Construction and analysis of educational tests using abductive machine learning,” Computers & Education, Vol. 51, No. 1, pp. 1-16, 2008.
[5]M. Badaracco and L. Martínez, “A fuzzy linguistic algorithm for adaptive test in Intelligent Tutoring System based on competences,” Expert Systems with Applications, Vol. 40, No. 8, pp. 3073-3086, 2013.
[6]A. M. Collins and M. R Quillian, “Retrieval time from semantic memory,” Journal of Verbal Learning and Verbal Behavior, Vol. 8, No. 2, pp. 240-248, 1969.
[7]D. E. Rumelhart and D. A. Norman, “Representation in memory,” In R. C. Atkinson, R. J. Herrnstein, G. Lindzey & R. D. Luce (Eds.). Stevens’ Handbook of Experimental psychology, 2nd Ed., New York, NY: Wiley, 1983.
[8]R. J. Koubek and N. Moutuhoy, “Toward a Model of Knowledge Structure and a Comparative Analysis of Knowledge Structure Measurement Techniques,” Wright State University, 1991, ED 3391719.
[9]J. Morton and D. Bekerian, “Three Ways of Looking at Memory,” In N. E. Sharkdy (ed.) Advances in cognitive science 1, 1986.
[10]D. H. Jonassen, K. Beissner, and M. Yacci, “Structural knowledge: Techniques for Representing Conveying, and Acquiring Structural Knowledge,” Hillsdale, NJ: Lawrence Erlbaum Associates, 1993.
[11]J. Appleby, P. Samules, and T. Treasure-Jones, “Diagnosys - a Knowledge-based Diagnostic Test of Basic Mathematical Skills,” Computers & Education, Vol. 28, No. 2, pp. 113-131, 1997.
[12]T. M. Haladyna, “Developing and validating multiple-choice exam items, 2nd ed.,” Mahwah, NJ: Lawrence Erlbaum Associates, 1999.
[13]H. K. Suen, “Principles of exam theories,” Hillsdale, NJ: Lawrence Erlbaum Associates, 1990.
[14]F. M. Lord, “Applications of Item Response Theory to Practical Testing Problems,” Hillsdale, NJ: Lawrence Erlbaum Associates, 1980.
[15]F. M. Lord , “Practical Applications of Item Characteristic Curve Theory,” Journal of Educational Measurement, Vol. 14, No. 2, pp. 117-138, 1977.
[16]G. Rasch, “Probabilistic models for some intelligence and attainment tests,” Copenhagen: The Danish Institute for Educational Research, 1960.
[17]A. Birnbaum, “Some latent trait models and their use in inferring an examinee’s stability,” In F. M. Lord, & M. R. Novick (Eds.), Statistical theories of mental test scores, Reading, MA: Addison-Wesley, 1968.
[18]J. Kennedy and R. C. Eberhart, “Particle Swarm Optimization,” Proceedings of the IEEE International Conference on Neural Networks, Vol. 4, pp. 1942-1948, 1995.
[19]T.-C. Huang, Y.-M. Huang, and S. C.-Cheng, “Automatic and Interactive e-Learning Auxiliary Material Generation Utilizing Particle Swarm Optimization,” Expert Systems with Applications, Vol. 35, No 4, pp. 2113-2122, 2008.
[20]Y.-T. Lin, Y.-M. Huang, and S.-C. Cheng, “An Automatic Group Composition System for Composing Collaborative Learning Groups Using Enhanced Particle Swarm Optimization,” Computers & Education, Vol. 55, No. 4, pp. 1483-1493, 2010.
[21]T.-C. Huang, S.-C. Cheng, and Y.-M. Huang, “A Blog Article Recommendation Generating Mechanism Using an SBACPSO Algorithm,” Expert Systems with Applications, Vol. 36, No. 7, pp. 10388-10396, 2009.
[22]Y. Shi and R. Eberhart, “Parameter Selection in Particle Swarm Optimization,” Lecture Notes in Computer Science, Vol. 1447, pp. 591-600, 1998.
[23]M. Clerc and J. Kennedy, “The Particle Swarm - Explosion, Stability, and Convergence in a Multidimensional Complex Space,” IEEE Transactions on Evolutionary Computation, Vol. 6, No. 1, pp. 58-73, 2002.
[24]Z.-H. Zhan, J. Zhang, Y. Li, and H. S.-H. Chung, “Adaptive Particle Swarm Optimization,” IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics, Vol. 39, No. 6, pp. 1362-1381, 2009.
[25]C. Li and S. Yang, “An Adaptive Learning Particle Swarm Optimizer for Function Optimization,” 2009 IEEE Congress on Evolutionary Computation, pp. 381-388, 2009.
[26]L. Mussi, F. Daolio, and S. Cagnoni, “Evaluation of parallel particle swarm optimization algorithms within the CUDA™ architecture,” Information Sciences, Vol. 181, No. 20, pp. 4642-4657, 2011.
[27]X. Chen and Y. Li, “A Modified PSO Structure Resulting in High Exploration Ability With Convergence Guaranteed,” IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics, Vol. 31, No. 5, pp. 1271-1289 , 2007.
[28]L. Liu, S. Yang, and D. Wang, “Particle Swarm Optimization with Composite Particles in Dynamic Environments,” IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics, Vol. 40, No. 6, pp. 1634-1648, 2010.
[29]S. Kiranyaz, T. Ince, A. Yildirm, and M. Gabbouj, “Fractional Particle Swarm Optimization in Multi-dimensional Search Space,” IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics, Vol. 40, No. 2, pp. 298-319, 2010.
[30]M. R. AlRashidi and M. E. El-Hawary, “A Survey of Particle Swarm Optimization Applications in Electric Power Systems,” IEEE Transactions on Evolutionary Computation, Vol. 13, No. 4, pp. 913-918, 2009.
[31]S. Dutta and S. P. Singh, “Optimal Rescheduling of Generators for Congestion Management Based on Particle Swarm Optimization,” IEEE Transactions on Power Systems, Vol. 23, No. 4, pp. 1560-1569, 2008.
[32]G.-G. Yen and W.-F. Leong, “Dynamic Multiple Swarms in Multi-objective Particle Swarm Optimization,” IEEE Transactions on Systems, Man, and Cybernetics, Part A: Systems and Humans, Vol. 39, No. 4, 2009, pp.890-911.
[33]C.-K. Goh, K.-C. Tan, D.-S. Liu, and S.-C. Chiam, “A competitive and cooperative co-evolutionary approach to multi-objective particle swarm optimization algorithm design,” European Journal of Operational Research, Vol. 202, No. 1, pp. 42-54, 2010.
[34]D.-S. Liu, K.-C. Tan, S.-Y. Huang, C.-K. Goh, and W.-K. Ho, “On solving multi-objective bin packing problems using evolutionary particle swarm optimization,” European Journal of Operational Research, Vol. 190, No. 2, pp. 357-382, 2008.
[35]D.-S. Liu, K.-C. Tan, C.-K. Goh, and W.-K. Ho, “A multi-objective memetic algorithm based on particle swarm optimization,” IEEE Transactions on Systems, Man and Cybernetics, Part B: Cybernetics, Vol. 37, No. 1, pp. 42-50, 2007.
[36]J. Sim and CC. Wright, “The kappa statistic in reliability studies: use, interpretation, and sample size requirements,” Phys Ther, Vol. 85, No. 3, pp. 257-268, 2005.
[37]吳德虎，以知識結構為基礎的動態評量適性診斷系統之研發-以五年級小數乘法單元為例，亞洲大學資訊工程學系碩士論文，民98年。
[38]白曉珊，以知識結構及貝氏網路為基礎之數學教材及電腦適性化測驗，國立臺中教育大學教育測驗統計研究所碩士論文，民97年。
[39]林立敏，連結不同知識結構之電腦適性學習系統研發，國立臺中教育大學教育測驗統計研究所碩士論文，民95年。
[40]余民寧，教育測驗與評量—成就測驗與教學評量，台北：心理出版社，民86年。
[41]余民寧，心理與教育統計學(修訂二版)，台北：三民書局，民94年。
[42]林晉榮，以知識結構為基礎的線上電腦適性測驗題庫系統，台中健康暨管理學院資訊科技研究所碩士論文，民92年。
[43]郭生玉，心理與教育測驗，臺北市：精華書局，民85年。
[44]吳佳儒，電腦化適性預試對試題難度估計精準度之影響，國立臺灣師範大學教育心理與輔導學系碩士論文，民99年。
[45]潘逸峻，以粒子群最佳化演算法結合知識結構於適性化測驗選題之研究，南台科技大學資訊工程研究所碩士論文，民100年。
[46]林建福，以知識結構及貝氏網路為基礎進行國小五年級小數乘法單元課程設計與評量建構之研究─以彰化縣某國小為例，國立臺中教育大學數學教育學系碩士論文，民97年。
[47]江啟明，二階段試題之貝氏網路與電腦化測驗研發，國立臺中教育大學教育測驗統計研究所碩士論文，民100年。
[48]張俊欽，以a-鄰近法為選題策略之電腦化適性測驗系統，亞洲大學資訊工程學系碩士論文，民94年。
[49]錢永財，以a-鄰近法為選題策略之電腦化適性測驗模擬研究，國立臺中教育大學教育測驗統計研究所碩士論文，民96年。
[50]廖英宏，利用改良式基因演算法於選題策略之研究，國立台灣科技大學電子工程系碩士論文，民93年。
[51]程千芬，運用進階基因演算法於選題策略之研究，國立臺南大學資訊教育研究所碩士論文，民92年。
[52]林哲鋒，應用混合式田口基因演算法於選題策略之研究，國立臺南大學數位學習科技學系碩士論文，民97年。
[53]李濠，雲端運算應用於試題分析與選題策略，統計資訊學系應用統計碩士論文，民101年。