ISSN 0439-755X
CN 11-1911/B
主办：中国心理学会
　　　中国科学院心理研究所
出版：科学出版社

心理学报 ›› 2015, Vol. 47 ›› Issue (3): 417-426.doi: 10.3724/SP.J.1041.2015.00417

• 论文 • 上一篇    

使用似然比D2统计量的题目属性定义方法

喻晓锋1,2;罗照盛1;高椿雷1;李喻骏1;王 睿1;王钰彤1   

  1. (1江西师范大学心理学院, 南昌 330022) (2亳州师范高等专科学校, 亳州 236800)
  • 收稿日期:2014-04-24 发布日期:2015-03-25 出版日期:2015-03-25
  • 通讯作者: 罗照盛, E-mail: luozs@126.com
  • 基金资助:

    国家自然科学基金(31160203, 31100756, 31360237)、国家社会科学基金(12BYY055)、教育部人文社会科学研究青年基金项目(13YJC880060)、安徽省高校省级优秀青年人才基金重点项目(2013SQRL127ZD)、安徽省自然科学研究项目(KJ2010B123, KJ2013B151)、高等学校博士学科点专项科研基金(20113604110001)、江西省研究生创新专项基金(YC2013-B024)和安徽省哲学社会科学规划项目(AHSKY2014D102)资助。

An Item Attribute Specification Method Based On the Likelihood D2 Statistic

YU Xiaofeng1,2; LUO Zhaosheng1; GAO Chunlei1; LI Yujun1; WANG Rui1; WANG Yutong1   

  1. (1 School of Psychology, Jiangxi Normal University, Nanchang 330022, China) (2 Computer Department, Bozhou Normal College, Bozhou 236800, China)
  • Received:2014-04-24 Online:2015-03-25 Published:2015-03-25
  • Contact: LUO Zhaosheng, E-mail: luozs@126.com

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摘要：

题目属性的定义是实施认知诊断评价的关键步骤, 通过有丰富经验的领域专家对题目的属性进行定义是当前的主要方法, 然而该方法受到许多主观经验因素的影响。寻找客观的题目属性定义或验证方法可以为主观定义过程提供策略支持或对结果进行改进, 因此已经引起研究者们的关注。本研究构建了一种简单高效的题目属性定义方法, 研究使用似然比D2统计量从作答数据中估计题目属性的方法, 实现属性掌握模式、题目参数和题目属性向量的联合估计。模拟研究结果表明, 使用似然比D2统计量可以有效地识别题目的属性向量, 该方法一方面可以实现新编制题目属性向量的在线估计, 另一方面可以验证已经定义的题目属性向量的准确性。

关键词: 题目属性定义, DINA模型, 似然比, 在线估计

Abstract:

The Q-matrix is a very important component of cognitive diagnostic assessments, and it maps attributes to items. Cognitive diagnostic assessments infer the attribute mastery pattern of respondents based on item responses. In a cognitive diagnostic assessment, item responses are observable, whereas respondents’ attribute mastery pattern is potentially, but not immediately observable. The Q-matrix plays the role of a bridge in cognitive diagnostic assessments. Therefore, Q-matrix impacts the reliability and validity of cognitive diagnostic assessments greatly. Research on how the errors of Q-matrix affect parameter estimation and classification accuracy showed that the Q-matrix from experts’ definition or experience was easily affected by experts’ personal judgment, leading to a misspecified Q-matrix. Thus, it is important to find more objective Q-matrix inference methods. This paper was inspired by Liu, Xu and Ying’s (2012) algorithm and the item-data fit statistic G2 in the item response theory framework. Further research on the Q-matrix inference, an online Q-matrix estimation method based on the statistic D2 was proposed in the present study. Those items which are the base of the online algorithm are called as base items, and it is assumed that the base items are correctly pre-specified. The online estimation algorithm can jointly estimate item parameters and item attribute vectors in an incrementally manner. In the simulation studies, we considered the DINA model with different Q-matrix (attribute-number is 3, 4 and 5), different sample size (400, 500, 800 and 1000), and different number of correct items (8, 9, 10, 11 and 12) in the initial Q-matrix. The attribute mastery pattern of the sample followed a uniform distribution, and the item parameters followed a uniform distribution with interval [0.05, 0.25]. The results indicated that: when the number of base items was not too small, the online estimation algorithm with the D2 statistic could estimate the attribute vectors of rest items one by one, and further improve the estimation by using the joint estimation. When item parameters were unknown, item number was 20, and item attributes was 3, 4 or 5, based on the initial Q-matrix, the online estimation algorithm could recover the true Q-matrix with a high probability even when the number of base items were as small as 8.

Key words: item attribute specification, DINA model, likelihood ratio, online estimation