拓广分部评分模型（GPCM）及应用EM算法的参数估计研究
摘要
项目反应理论(IRT)是世界教育与心理测量理论发展的重要趋势，也日益成为当今测验领域的一个热点问题。本文探讨的是IRT理论中的一个重要评分模型GPCM。在理论部分详细论述了GPCM模型的逻辑结构、适用范围，指出了它与其它几种重要模型之间的关系及异同之处。在理论与实际结合部分就如何应用EM算法开发具有实用价值的软件进行了初步的尝试。
IRT is the important trend of educational and psychological measurement around the world ,and it is also increasingly becoming a hotspot in current testing fieldso A important scoring model of IRT is discussed in this article ?In the theoretic session of this article ,the logic structure ^ the application domain of GPCM are presented in details and it also points out the relations and differences between GPCM and several important Models in IRT; the application session of this article is trying to exploring a program with EM algorithm about GPCM o
IRT is the important trend of educational and psychological measurement around the world ,and it is also increasingly becoming a hotspot in current testing fieldso A important scoring model of IRT is discussed in this article ?In the theoretic session of this article ,the logic structure ^ the application domain of GPCM are presented in details and it also points out the relations and differences between GPCM and several important Models in IRT; the application session of this article is trying to exploring a program with EM algorithm about GPCM o
引文
1、朱本仁编著．蒙特卡罗方法引论．山东大学出版社
2、[苏联]Н．П．布斯近科，Ю．А．施廖盖尔．王毓云，杜淑敏译．统计试验方法．上海科学技术出版社
3、复旦大学数学系主编．概率论与数理统计．上海科技出版社
4、蔡大用．白峰杉．高等数值分析．清华大学出版社
5、张厚粲．心理与教育统计学．北京大学出版社
6、漆书青，戴海崎，丁树良．现代教育与心理测量学原理．江西教育出版社
7、中国科学院沈阳计算机技术研究所，后字四一四部队，北京工业大学计算站 编．电子计算机常用算法(增订版)．科学出版社
8、李庆扬，莫孜中，祁力群．非线性方程组的数值解法．科学出版社
9、冯果忱．非线性方程组迭代解法．上海科技出版社
10、王德人．非线性方程组解法与最优化方法． 人们教育出版社
11、肖云茹．概率统计计算方法．南开大学出版社
12、J．P．戴斯，J．A．纳格利尔里，J．R．．柯尔比．杨艳云，谭和平译．认知过程的评估——智力的PASS理论．华东师范大学出版社
13、余嘉元．项目反应理论中若干模型的比较．心理学报，1990
14、欧东明．项目反应理论(IRT)中应用EM算法进行参数估计．毕业论文
15、许志勇．IRT多级反应模型：现状与项目分析实践．毕业论文
16、Eiji Muraki, R. Darrel Bock. PARSCALE. SSI SCIENTIFIC SOFTWARE INTERNATIONAL
17、David Woodruff, Bradley A. Hanson. Estimation for Item Response Models using the EM Algorithm for Finite Mixtures. Presented at the Annual Meeting of the Psychometric Society, Gatlinburg, Tennessee, June, 1997.
18、Frank B. Baker, Marcel Dekker. Item Response Theory. Inc. New York.
19、Ronald K. Hambleton, Wim J. Van der Linden. Handbook of Modern Item Response Theory. Springer
20、Eiji Muraki. A Generalized Partial Credit Model: Application of an EM Algorithm. Educational Testing Service
21、David woodruff, Bradley A. Hanson. Estimation for Item Response Models using the EM Algorithm for Finite Mixtures. Presented at the Annual Meeting of the Psychometric Society, Gatlinburg, Tennessee, June, 1997
22、Lord,F. M. Applications of Item Response Theory to practical testing problems. Hillsdale, NJ:Lawrence Erlbaum Associates, 1980
23、Brad Hanson. IRT Parameter Estimation using the EM Algorithm. Psychometrika,35,179-197, October 6,1998(revised 10/28/98)
24、Chuan Hai Liu, Donald,B. Rubin. Parameter Epansion to accelerate EM:The PX-EM Algorithm. Biometrika,85,4,pp 755-770, 1998
2、[苏联]Н．П．布斯近科，Ю．А．施廖盖尔．王毓云，杜淑敏译．统计试验方法．上海科学技术出版社
3、复旦大学数学系主编．概率论与数理统计．上海科技出版社
4、蔡大用．白峰杉．高等数值分析．清华大学出版社
5、张厚粲．心理与教育统计学．北京大学出版社
6、漆书青，戴海崎，丁树良．现代教育与心理测量学原理．江西教育出版社
7、中国科学院沈阳计算机技术研究所，后字四一四部队，北京工业大学计算站 编．电子计算机常用算法(增订版)．科学出版社
8、李庆扬，莫孜中，祁力群．非线性方程组的数值解法．科学出版社
9、冯果忱．非线性方程组迭代解法．上海科技出版社
10、王德人．非线性方程组解法与最优化方法． 人们教育出版社
11、肖云茹．概率统计计算方法．南开大学出版社
12、J．P．戴斯，J．A．纳格利尔里，J．R．．柯尔比．杨艳云，谭和平译．认知过程的评估——智力的PASS理论．华东师范大学出版社
13、余嘉元．项目反应理论中若干模型的比较．心理学报，1990
14、欧东明．项目反应理论(IRT)中应用EM算法进行参数估计．毕业论文
15、许志勇．IRT多级反应模型：现状与项目分析实践．毕业论文
16、Eiji Muraki, R. Darrel Bock. PARSCALE. SSI SCIENTIFIC SOFTWARE INTERNATIONAL
17、David Woodruff, Bradley A. Hanson. Estimation for Item Response Models using the EM Algorithm for Finite Mixtures. Presented at the Annual Meeting of the Psychometric Society, Gatlinburg, Tennessee, June, 1997.
18、Frank B. Baker, Marcel Dekker. Item Response Theory. Inc. New York.
19、Ronald K. Hambleton, Wim J. Van der Linden. Handbook of Modern Item Response Theory. Springer
20、Eiji Muraki. A Generalized Partial Credit Model: Application of an EM Algorithm. Educational Testing Service
21、David woodruff, Bradley A. Hanson. Estimation for Item Response Models using the EM Algorithm for Finite Mixtures. Presented at the Annual Meeting of the Psychometric Society, Gatlinburg, Tennessee, June, 1997
22、Lord,F. M. Applications of Item Response Theory to practical testing problems. Hillsdale, NJ:Lawrence Erlbaum Associates, 1980
23、Brad Hanson. IRT Parameter Estimation using the EM Algorithm. Psychometrika,35,179-197, October 6,1998(revised 10/28/98)
24、Chuan Hai Liu, Donald,B. Rubin. Parameter Epansion to accelerate EM:The PX-EM Algorithm. Biometrika,85,4,pp 755-770, 1998