IRT中最小化χ~2/EM参数估计方法  

Minimum Chi-square/EM Estimation Under IRT

作　　者：朱玮[1] 丁树良[2] 陈小攀[3] 

机构地区：[1]深圳市档案局,深圳518000 [2]江西师范大学信息与计算机工程学院,南昌330027 [3]江西师范大学传播学院,南昌330027

出　　处：《心理学报》2006年第3期453-460,共8页Acta Psychologica Sinica

基　　金：国家自然科学基金(60263005);江西省自然科学基金(0411021);全国教育科学规划重点课题(DBB010501);省教育厅科技项目;江西省分布计算工程技术研究中心的资助(江西师范大学)

摘　　要：对IRT的双参数Logistic模型(2PLM)中未知参数估计问题,给出了一个新的估计方法??最小化χ2/EM估计。新方法在充分考虑项目反应理论(IRT)与经典测量理论(CTT)之间的差异的前提下,从统计计算的角度改进了Berkson的最小化χ2估计,取消了Berkson实施最小化χ2估计时需要已知能力参数的不合实际的前提,扩大了应用范围。实验结果表明新方法能力参数的估计结果与B ILOG相比,精确度要高,且当样本容量超过2000时,项目参数的估计结果也优于B ILOG。实验还表明新方法稳健性好。A new parameter-estimation method, the minimum X^2/EM algorithm for unknown parameters of the 2PLM, was proposed. The new estimation paradigm was based on careful considerations of the differences between item response theory （IRT） and classical test theory （cTr）. Specifically, it is derived from a modified version of the minimum X^2algorithm originally proposed by Berkson （1955）. The starting point of the minimum X^2 algorithm is the Pearson X^2. Given ability score level, examinees can be classified into K categories; the congruence of the sample and the expected distribution can be measured by X^2 statistic. The subsequent estimation procedure is to seek appropriate item parameters to minimize X^2. Because true ability scores are unobservable, most of the time, examinees are classified according to observed scores. We believe this practice is based on the point of view of CTT, which assumes that the examinees with the same observed scores have the same ability scores. As we all know, the posterior distribution of ability parameter is affected by item parameters. Thus, the new method takes the posterior distribution of ability parameter into account and introduces artificial data in the EM algorithm for estimating the unknown parameters in IRT models. The new method redefinesPye, rye （ the observed proportion of correct responses and incorrect responses） of Berkson＇ s minimum X^2 algorithm, and replaces it with artificial datum rye/fye and rye respectively. The statistical reasoning and operations behind this method can be intuitively explained as the following： In the minimum X^2 algorithm, the observed proportion of responses is fixed and the theoretical distribution is changed with the new estimated value of the unknown parameters. In other words, the algorithm draws the theoretical distribution closer to the observed distribution and, as a consequence, the estimating speed slows down. In order to accelerate estimation, the new method connects artificial data to the item parameters t

关 键 词：项目反应理论 参数估计 EM算法 

分 类 号：B841[哲学宗教—基础心理学]