ISSN 0439-755X
CN 11-1911/B

心理学报 ›› 2016, Vol. 48 ›› Issue (5): 588-598.doi: 10.3724/SP.J.1041.2016.00588

• 论文 • 上一篇    

改进的认知诊断模型项目功能差异检验方法 ——基于观察信息矩阵的Wald统计量


  1. (1北京师范大学发展心理研究所, 北京 100875) (2中国基础教育质量监测协同创新中心, 北京 100875) (3泰山学院教师教育学院, 山东泰安 271000)
  • 收稿日期:2015-09-17 出版日期:2016-05-25 发布日期:2016-05-25
  • 通讯作者: 辛涛, E-mail:
  • 基金资助:

    国家自然科学基金面上项目(31371047); 中央高校基本科研业务费专项资金资助(SKZZX2013028)。

An improved method for differential item functioning detection in cognitive diagnosis models: An application of Wald statistic based on observed information matrix

LIU Yanlou1; XIN Tao1,2; LI Lingqing3; TIAN Wei2; LIU Xiaoxiao1   

  1. (1 Institute of Developmental Psychology, Beijing Normal University, Beijing 100875, China) (2 National Innovation Center for Assessment of Basic Education Quality, Beijing 100875, China) (3 School of Teacher Education, Taishan University, Taian 271000, China)
  • Received:2015-09-17 Online:2016-05-25 Published:2016-05-25
  • Contact: XIN Tao, E-mail:


Hou, de la Torre和Nandakumar (2014)提出可以使用Wald统计量检验DIF, 但其结果的一类错误率存在过度膨胀的问题。本研究中提出了一个使用观察信息矩阵进行计算的改进后的Wald统计量。结果表明:(1)使用观察信息矩阵计算的这一改进后的Wald统计量在DIF检验中具有良好的一类错误控制率, 尤其是在项目具有较高区分能力的时候, 解决了以往研究中一类错误率过度膨胀的问题。(2)随着样本量的增加以及DIF量的增大, 使用观察信息矩阵计算Wald统计量的统计检验力也在增加。

关键词: Wald统计量, 项目功能差异, 认知诊断模型, 观察信息矩阵, 经验交叉相乘信息矩阵


In cognitive diagnostic models (CDMs), differential item functioning (DIF) refers to the probabilities of success of an item being different for examinees with the same attribute mastery pattern in the groups. The detection of DIF is an important step to ensure the fairness and validity of results from CDMs for all groups. Hou et al. (2014) proposed that the Wald statistic can be used to detect DIF in CDMs. Unfortunately, their results revealed that the Wald statistic based on the information matrix estimation method developed by de la Torre (2009, 2011) yielded inflated Type I error rates. However, Li and Wang (2015) found that the Type I error rates of the Wald statistic in which MCMC algorithms were implemented were slightly inflated in their study under the same conditions. In this study, we proposed an improved Wald statistic based on the observed information matrix for DIF assessment. As a general demonstration, we took the log-linear cognitive diagnosis model (LCDM; Henson et al., 2009) as an example. In this simulation study, in order to compare the results with previous studies (e.g., Hou et al.,2014; Li & Wang, 2015), we followed the simulation design used by Hou et al. (2014), except that we implemented the observed or cross-product (XPD) information matrix in the Wald statistic computation. Parameters set in the studies were: the test length at 30, the number of attributes at 5, and the maximum number of required attributes for an item at 3. Binary item response data were generated from the DINA model. Three sets of true item parameter values were considered for the reference group. Two DIF sizes: .05 and .10, and two types of DIF: uniform and nonuniform, were manipulated. Two sample sizes were considered, 500 and 1,000. Each condition was replicated 1000 times, and the estimation code was written in R (R Core Team, 2015). The simulation results showed that: (1) for the relatively discriminating items, Wald statistic had accurate Type I error control when the observed information matrix was used in its computation. However, when the slip and guessing parameters were large , the Type I error control was slightly conservative. (2) When the XPD information matrix was used for the computation of the Wald statistic, the Type I error control was conservative; that is, the performance of the observed information matrix was better than the XPD information matrix. (3) The number of attributes required for success on the item did not have a notable impact on the Type I error control of Wald statistic, irrespective of whether the observed or the XPD information matrix was used for the statistic. (4) The power rates of Wald statistic for detecting DIF increased as the sample size increased. We conclude that our improved Wald statistic provided follows asymptotically a chi-square distribution with degrees of freedom equal to 2, for DINA model. The improved Wald statistic is a useful and powerful tool for DIF detection in CDMs.

Key words: Wald statistic, differential item functioning, cognitive diagnosis model, observed information matrix, cross-product information matrix