【作者】 罗芬；

【导师】 丁树良；

【作者基本信息】 江西师范大学 ， 计算机应用， 2003， 硕士

【摘要】 本文在项目反应理论(IRT)框架下，就目前流行的参数估计方法进行分析比较，提出一种新方法——双重两步迭代估计。新方法将经验Logistic回归用于两参数Logistic模型的参数估计，使用logit变换建立线性模型，利用线性模型的最小二乘估计得到第j个项目的项目参数向量β_j=(α_j，λ_j)′的两步估计由于X_j含有未知的讨厌参数θ，∑的理论值也和θ有关，我们结合上式的结果对θ进行再估计。修正θ进而修正X_j和∑，从而形成一种新的估计方法—双重两步迭代估计蒙特卡洛模拟结果显示，双重两步迭代估计提高了估计对真值的恢复能力。这种新方法有以下三个优点：①项目数很少时参数估计的结果也较稳定；②能处理测验中含有少量特殊反应模式(见第二章)的参数估计；③以估计值和真值之差的绝对值(平方)的平均值作为估计对真值的修复能力为指标，新方法的参数估计结果与同类流行软件相比，修复能力不相上下；特别地，新的参数估计方法可以用于多级评分项目GPCM，并为估计题组项目开辟了另一条道路。更多还原

【Abstract】 In this thesis, based on Item Response Theory, a number of ways to estimate the latent trait and item parameters were introduced and their advantages and disadvantages were analyzed; what is more, Empirical Logistic regression and two parameters Logistic model (2PLM) are combined to set up a linear model by logit-mapping and a new parameter-estimation method is proposed. The least square estimation in linear model is used to derive the two-stage estimation of the item parameter vector β1 of j th item as follows:Noting that Xj consists of the nuisance parameters θs , ∑j,βj, were updated so that the estimation of 6 s could be renewed. The above algorithm forms a double-two-stage iteration, as following:The results of Monte Carlo stimulation show that the double-two-stage iteration algorithm is more effective than empirical Logistic regression after item and ability parameters recovery study. There are three advantages about the new method: first . the new method can be applied to estimate fewer items; secondly, a test including fewer unusual response patterns can also be evaluated; thirdly, the results compared with homogeneous software dealing with 2PLM are accepted using mean absolute error as the criterion. Further, the linear model and new method could be expanded the situation when polytomous items and items in the testlet are display in a test.更多还原