项目反应理论（IRT）中等值方法及其比较
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摘要
等值的研究对于考试的公平性、题库建设、教学质量评价和计算机化自适应测验具有重要的意义。等值的一项主要工作是估计等值系数。本文在项目反应理论(Item Response Theory,IRT)框架下提出了一种抽象形式将目前已有的各种等值系数估计方法统一表示，通过统一表示找出了各种等值方法之间的关系，并导出了几种新的等值方法，其中包括相对熵(Relative Entropy)等值法和对数对照(Logcontrast)等值法。另外，由于等值系数的估计计算繁杂冗长，本文将几种等值方法的求解进行了统一处理，不仅提高了计算效率，而且为等值方法的比较提供了前提条件。最后，由于等值方法优劣的比较是等值研究的重要内容，但迄今为止没有一个合理的比较标准，为了比较新导出的等值方法和原有等值方法之间的优劣，本文给出了一种客观的比较标准——Monte_Carlo模拟，结合偏移平均平方根(Root Square Mean Deviation,RMSD)和Wilcoxon符号秩检验，将各种等值方法进行了客观的比较分析。模拟结果表明，新等值方法一般不比目前流行的等值方法差，有时甚至更理想。
The research on test equating is very important for test equity,item banking,teaching quality assessing,and computerized adaptive test. First,one main work of test equating is to estimate equating coefficients,In the paper in the light of Item Response Theory an abstract form is introduced,which makes all test equating methods in uniform,by the abstract form,the relationships among the existed methods being found out,and some new methods being derived,including Relative Entropy equating method and Logcontrast equating method. Second,the procedure of estimating test equating coefficients may be dull or complex,in this thesis,a uniform procedure,which not only improve the computing efficiency,but also is the base of comparison of various equating methods,is given. Third,because the comparison of equating methods is a major part on test equating research,there is not a reliable criterion up to now,in order to compare the new methods with the existing ones,in this thesis an objective approach is given. The new a
pproach consists of three steps:1. making Monte Carlo simulation;2." computing Root Square Mean Deviation (RMSD) of outcome in Monte Carlo studies;3. using Wilcoxon signed ranks test to analyze RMSD. The results having been compared show that the new methods are as good as those existing ones,even better in some case in view of statistics.
The research on test equating is very important for test equity,item banking,teaching quality assessing,and computerized adaptive test. First,one main work of test equating is to estimate equating coefficients,In the paper in the light of Item Response Theory an abstract form is introduced,which makes all test equating methods in uniform,by the abstract form,the relationships among the existed methods being found out,and some new methods being derived,including Relative Entropy equating method and Logcontrast equating method. Second,the procedure of estimating test equating coefficients may be dull or complex,in this thesis,a uniform procedure,which not only improve the computing efficiency,but also is the base of comparison of various equating methods,is given. Third,because the comparison of equating methods is a major part on test equating research,there is not a reliable criterion up to now,in order to compare the new methods with the existing ones,in this thesis an objective approach is given. The new a
pproach consists of three steps:1. making Monte Carlo simulation;2." computing Root Square Mean Deviation (RMSD) of outcome in Monte Carlo studies;3. using Wilcoxon signed ranks test to analyze RMSD. The results having been compared show that the new methods are as good as those existing ones,even better in some case in view of statistics.
引文
[1]戴海崎：等级反应模型项目特征曲线法等值研究。心理学探新 2000,Vol．20，No．3，49-53．
[2]甘登文、丁晖、洪少南、丁树良：概率论与数理统计。江西教育出版社，2000。
[3]黄明和、周定康、谢旭升、李云清：数据结构。江西教育出版社，1998。
[4]李善茂、杜大鹏、刘国宏：Visual Basic 6.0 高级编程技巧。电子工业出版社，1999
[5]刘振亚：计量经济学教程。中国人民大学出版社，1997。
[6]罗札．塞克斯著、罗永泰、史道济译：应用统计手册。天津科技翻译出版公司，1988
[7]茆诗松、王静龙、濮晓龙：高等数理统计。高等教育出版社、施普林格出版社，1998
[8]毛一心：Visual ForPro6.0应用及实例集锦。人民邮电出版社，2000
[9]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，1998
[10]王玲玲、周纪芗：常用统计方法。华东师范大学出版社，1994
[11]王能超：数值分析简明教程。高等教育出版社，1995
[12]王则柯：计算的复杂性。湖南教育出版社，1993。
[13]吴喜之：非参数统计方法。高等教育出版社，1996
[14]肖云茹：概率统计计算方法。南开大学出版社，1994
[15]谢小庆：对15种测验等值方法的比较研究。心理学报，2000，Vol．32，No．2：217-223。
[16]张益新、沈雁：算法引论。国防科技大学出版社，1999。
[17]邹海明、余祥宣：计算机算法基础。华中理工大学出版社，1995
[18]Hambleton,R.K.Swaminathan,H.Item Response Theory:Principles and Applications. Boston:Klumer_Nijhoff publishing. 1985.
[19]Han T, Kolen M. A comparison among IRT true-and observed-score equatings and traditional equipercentile equating .Applied Measurement in Education, 1997
[20]Kim,S-H,& Cohen,A.S. A minimum χ~2 method for equating tests under the graded response model. Applied psychological measurement Vol.19,No.2,167-176,1995
[21]Kolen,M.J.& Brennam,R.L. Test Equating, Methods and Practices,New York: Springer-Verlag, 1995
[22]Michael Harwell,Clement A.Stone,Tse_chi Hsu,and Levent Kirisci:Monte Carlo Studies in Item Response Theory . Applied Psychological Measurement Vol.20,No.2,1996,pp. 101-125.
[23]Michael R.Harwell:Analyzing the Results of Monte Carlo Studies in Item Response Theory. Educational and Psychological Measurement, Vol.57,No.2,1997,pp.266-279.
[24]Paul W. Holland,Donald B.Rubin: Test Equating. Academic Press, 1982
[25]Samuel Kotz(Ed): Encyclopedia of Statistical Sciences, Volume 4,P421-P425 :John Wiley & Sons, New York, 1983.
[2]甘登文、丁晖、洪少南、丁树良：概率论与数理统计。江西教育出版社，2000。
[3]黄明和、周定康、谢旭升、李云清：数据结构。江西教育出版社，1998。
[4]李善茂、杜大鹏、刘国宏：Visual Basic 6.0 高级编程技巧。电子工业出版社，1999
[5]刘振亚：计量经济学教程。中国人民大学出版社，1997。
[6]罗札．塞克斯著、罗永泰、史道济译：应用统计手册。天津科技翻译出版公司，1988
[7]茆诗松、王静龙、濮晓龙：高等数理统计。高等教育出版社、施普林格出版社，1998
[8]毛一心：Visual ForPro6.0应用及实例集锦。人民邮电出版社，2000
[9]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，1998
[10]王玲玲、周纪芗：常用统计方法。华东师范大学出版社，1994
[11]王能超：数值分析简明教程。高等教育出版社，1995
[12]王则柯：计算的复杂性。湖南教育出版社，1993。
[13]吴喜之：非参数统计方法。高等教育出版社，1996
[14]肖云茹：概率统计计算方法。南开大学出版社，1994
[15]谢小庆：对15种测验等值方法的比较研究。心理学报，2000，Vol．32，No．2：217-223。
[16]张益新、沈雁：算法引论。国防科技大学出版社，1999。
[17]邹海明、余祥宣：计算机算法基础。华中理工大学出版社，1995
[18]Hambleton,R.K.Swaminathan,H.Item Response Theory:Principles and Applications. Boston:Klumer_Nijhoff publishing. 1985.
[19]Han T, Kolen M. A comparison among IRT true-and observed-score equatings and traditional equipercentile equating .Applied Measurement in Education, 1997
[20]Kim,S-H,& Cohen,A.S. A minimum χ~2 method for equating tests under the graded response model. Applied psychological measurement Vol.19,No.2,167-176,1995
[21]Kolen,M.J.& Brennam,R.L. Test Equating, Methods and Practices,New York: Springer-Verlag, 1995
[22]Michael Harwell,Clement A.Stone,Tse_chi Hsu,and Levent Kirisci:Monte Carlo Studies in Item Response Theory . Applied Psychological Measurement Vol.20,No.2,1996,pp. 101-125.
[23]Michael R.Harwell:Analyzing the Results of Monte Carlo Studies in Item Response Theory. Educational and Psychological Measurement, Vol.57,No.2,1997,pp.266-279.
[24]Paul W. Holland,Donald B.Rubin: Test Equating. Academic Press, 1982
[25]Samuel Kotz(Ed): Encyclopedia of Statistical Sciences, Volume 4,P421-P425 :John Wiley & Sons, New York, 1983.