ISSN 0439-755X
CN 11-1911/B

心理学报 ›› 2009, Vol. 41 ›› Issue (02): 175-181.

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Tatsuoka 矩阵理论的修正


  1. 江西师范大学计算机信息工程学院,南昌330027
  • 收稿日期:2007-10-24 修回日期:1900-01-01 出版日期:2009-02-28 发布日期:2009-02-28
  • 通讯作者: 丁树良

Modification of Tatsuoka’s Q Matrix Theory

DING Shu-Liang;ZHU Yu-Fang;LIN Hai-Jing;CAI Yan   

  1. Computer Information Engineering College of Jiangxi Normal University, Nanchang 330027, China
  • Received:2007-10-24 Revised:1900-01-01 Online:2009-02-28 Published:2009-02-28
  • Contact: DING Shu-Liang

摘要: K .K.Tatsuoka和她同事开发的规则空间模型(RSM)是一种在国内外有较大影响的认知诊断模型,但是Tatsuoka的RSM中 矩阵理论存在缺陷和错误,这些失误使得RSM中用布尔描述函数(BDF)计算被试理想项目反应模式(IRP)的方法缺乏理论依据。这里揭示了Tatsuoka的 矩阵理论的缺陷和错误并引进既不使用BDF又便于应用的计算IRP的方法;接着还介绍一种由可达阵计算简化 阵的方法,该方法显示了可达阵在构造认知诊断测验的重要性。这些结果对丰富 矩阵理论及正确使用RSM进行认知诊断有一定的意义

关键词: 规则空间模型, 属性层次模型, 矩阵理论, 理想反应模式, 扩张算法

Abstract: In Tatsuoka’s Rule Space Model (RSM) and in Attribute Hierarchy Method (AHM) (Leighton et al.,2004), attributes and hierarchy serve as the most important input variables to the model because they provide the basis for interpreting the results in this approach to psychometric modeling (Gierl, et al., 2000).The hierarchical relation among the attributes is represented by adjacency matrix. From the adjacency matrix, the reachability matrix could be derived, which may then play an important role for deriving the reduced Q matrix (Gierl, et al., 2000). The reduced Q matrix is used to derive the examinee’s knowledge state vector, which is a core concept in the Rule Space Model.
In this paper, some flaws of Tatsuoka’s Q matrix theory (1991, 1995) are discussed, and some remedies are proposed, especially through a series of new algorithms. These algorithms are useful in the Rule Space Model and in the Attribute Hierarchy Model to construct a Q matrix when the reachability matrix is given, and are useful to calculate the ideal/expected response patterns without using the Boolean Descriptive Function. These algorithms demonstrate two facts: firstly, the reachability matrix is the most important tool in constructing a cognitive test, and could help increase the diagnosis accuracy; secondly, use of these algorithms can remedy the flaws in the Tatsuoka’s Q matrix theory. Furthermore, the new algorithms have other advantages, such as that they reduce computational burden for some complicated tasks requiring heavy numerical operations. Hence, the proposed methods in the paper may enrich the applications of the Q matrix theory

Key words: rule space model, attribute hierarchy model, Q matrix theory, ideal response pattern, augment algorithm


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