ISSN 0439-755X
CN 11-1911/B

心理学报 ›› 2009, Vol. 41 ›› Issue (03): 267-275.

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  1. 江西师范大学计算机信息工程学院,南昌330027
  • 收稿日期:2007-12-25 修回日期:1900-01-01 出版日期:2009-03-30 发布日期:2009-03-30
  • 通讯作者: 丁树良

A Polytomous Extension of Attribute Hierarchy Method
Based on Graded Response Model

Zhu Yu-Fang;Ding Shu-Liang   

  1. Computer Information Engineering College of Jiangxi Normal University, Nanchang 330027, China
  • Received:2007-12-25 Revised:1900-01-01 Online:2009-03-30 Published:2009-03-30
  • Contact: Ding Shu-Liang

摘要: 给出基于等级反应模型的属性层级方法(Attribute Hierarchy Method, AHM),并简记为GRM-AHM,提出了相应的确定GRM-AHM的期望项目反应模式全集的方法和一种新的归类法LL。用蒙特卡洛模拟实验比较GRM-AHM的几种归类法的归准率(属性模式归准率和单个属性的平均判准率)。结果发现,新归类法的归准率与AHM中的方法A差不多,但比方法B高很多;随着被试作答失误率的提高,它们的归准率都有所下降。在归类精度和简单性方面,GRM-AHM都比Bolt等(2004)提出的多级评分融合模型(Fusion Model)好

关键词: 属性层级方法, 等级反应模型, 对数似然比

Abstract: The value of diagnostic assessment lies in its ability to reveal each student’s specific cognitive strengths and weaknesses and further helps design effective interventions for individual student. Leighton et al.(2004) proposed a cognitive diagnostic model called Attribute Hierarchy Method (AHM), which is based on the assumption that test items can be described by a hierarchically-ordered set of attributes. Attributes are defined as basis cognitive processes or skills required to solve test items correctly. Examinees’ attribute pattern can be estimated by classifying each observed response pattern into one of the expected response patterns, which can be clearly explained by the presence or absence of the attributes without any errors or “slip”. So far, AHM was has only been introduced based on dichotomous IRT models, where items used in classroom assessments or performance assessments usually involve open-ended or constructed responses., and there is an assumption that an item can be answered correctly if and only if all the attributes involved in the item can be answered correctly. It means that missing one attribute is equivalent to missing all required attributes.
Since accurate diagnosis requires a rich description of examinee test performance, and polytomous models can give more information for score than the dichotomous model, an extension of AHM for based on a particular polytomous model ¾ graded response model (GRM), is proposed, and a new classification method is introduced in this paper. Four kinds of attribute hierarchies were separately used as the basis for the simulation. For each of the four attribute hierarchies, a sample of 5000 expected item response vectors was generated to approximate a normal distribution, Given that samples only consist of expected response patterns which are free from slips, the observed item response patterns were generated by randomly adding slips to each of the expected response patterns. In this study, the percentage of random errors was manipulated to be 2%, 5%,10% and 15%, respectively, of the total number of item response in order to examine whether the percentage of random errors has an impact on the accuracy of classification methods. In order to generate 5% random errors, for example, a uniform probability of 0.05 was employed to randomly add slips. For each item, if random number less than 0.025, then the score of item subtract 1 provided the original score is not zero; if random number higher than 0.925, then the score of the item adds 1 whenever the original score is not full. Ability parameters and item parameters can be estimated using ANOTE 1.60.
Simulation results showed that the classification rate for LL is only slightly better than that of Method A, but clearly outperforms that of Method B. In addition, polytomous extension of AHM is better than the polytomous extension of the Fusion Model proposed by Bolt et al.(2004)in terms of the classification accuracy and simplicity.

Key words: attribute hierarchy method, graded response model, logarithm likelihood ratio


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