Logistic加权模型的理论构建与模拟分析  

The weighted-score logistic model and Monte Carlo simulation study

作　　者：简小珠[1,2] 戴步云[2] 戴海琦[2] 

机构地区：[1]井冈山大学教育学院,江西吉安343009 [2]江西师范大学心理学院,江西省心理与认知科学重点实验室,南昌330022

出　　处：《心理学报》2016年第12期1625-1630,共6页Acta Psychologica Sinica

基　　金：江西省社会科学规划青年项目(13JY47);江西省高校人文社会科学研究项目青年项目(XL1515);江西省博士后科研择优资助项目(2013KY51);新汉语水平考试课题(课题编号:1869)

摘　　要：试题难度、试题考查重要性程度加权是多级记分试题的两个基本属性,因而在IRT项目特征函数中需用不同参数来表示。以往多级记分模型用多个难度参数来描述多级记分试题的难度,不能有效的表达多级记分试题的分数权重作用。从多级记分试题的分数加权作用角度,本文提出Logistic加权模型并论述了理论构建思想。在Logistic加权模型下对项目参数估计的EM算法进行推导并编写了相应的参数估计程序。在Logistic加权模型下进行测验模拟,发现项目参数估计的模拟返真性能良好。Item difficulty and item emphases are the two fundamental properties for the polytomously scored item. Thus, it is necessary to use a special parameter, the weighted-score parameter or the item full mark, to express the emphases of the polytomously scored item. In the previous studies, the researchers had proposed eight polytomous models, e.g., Graded-Response Model, Partial Credit Model, etc. In all the polytomous models, several item difficult parameters are used to represent the item difficulty based on the dichotomous Logistic model. Thus, the polytomous models may not effectively give expression to the item emphases of the polytomous item. A new polytomous model, the weighted-score logistic model （WSLM）, is proposed in this study. On the basis of the item emphases of the polytomously scored item, the WSLM model adds the weighted-score parameters into the dichotomous logistic model. The WSLM includes only one difficulty parameter （i.e., the average difficulty parameter） to represent the overall item difficulty, which obviously differs from the other polytomous models. Moreover, in the WSLM, the probability of an examinee responding in category , is of certain functional relation with the average difficulty parameter, discrimination parameter, and the score that the examinee have obtained on this item. Thus, the probability of responding in category under the WSLM can be expressed as . According, the probabilities that an individual will receive the category scores of 0, 1, 2, …, under the WSLM are expressed by： respectively. And all the above probabilities add up to 1. Then, the probability that an examinee will receive a category score of or higher on a polytomously scored item is . It should be noted that, the WSLM reduces to the dichotomous logistic model if . Similarly, the probabilities of the WSLM can also be graphically represented via the category response curves and operating characteristic curves. What’s more, the shapes of the category response curves and operating characteristic curv

关 键 词：IRT LOGISTIC模型 Logistic加权模型 多级记分模型 

分 类 号：B841[哲学宗教—基础心理学]