ISSN 0439-755X
CN 11-1911/B

心理学报 ›› 2022, Vol. 54 ›› Issue (9): 1122-1136.doi: 10.3724/SP.J.1041.2022.01122

• 研究报告 • 上一篇    下一篇


童昊1, 喻晓锋1(), 秦春影2, 彭亚风1, 钟小缘1   

  1. 1江西师范大学心理学院, 南昌 330022
    2南昌师范学院数学与信息科学学院, 南昌 330032
  • 收稿日期:2021-08-05 发布日期:2022-07-21 出版日期:2022-09-25
  • 通讯作者: 喻晓锋
  • 基金资助:

Detection of aberrant response patterns using a residual-based statistic in testing with polytomous items

TONG Hao1, YU Xiaofeng1(), QIN Chunying2, PENG Yafeng1, ZHONG Xiaoyuan1   

  1. 1School of Psychology, Jiangxi Normal University, Nanchang, 330022, China
    2School of Mathematics and Information Science, Nanchang Normal University, Nanchang 330032, China
  • Received:2021-08-05 Online:2022-07-21 Published:2022-09-25
  • Contact: YU Xiaofeng


本文提出一种多级计分项目下的个人拟合统计量R, 考察它在检测6种常见的异常作答模式(作弊、猜测、随机、粗心、创新作答、混合异常)下的表现, 并与标准化对数似然统计量lzp进行比较。结果表明:(1) 在异常作答覆盖率较低并且异常作答类型为作弊和猜测时, R的检测率显著高于lzp; (2) 随着测验长度和被试异常程度的增加, 两种统计量的检测率都会上升; (3) 在一些条件下, Rlzp检测效果接近。实证数据分析进一步展示了R统计量的使用方法和过程, 结果也表明R统计量具有较好的应用前景。

关键词: 多级计分项目, 项目反应理论, 个人拟合统计量, 异常行为检测, 等级反应模型


Tests are widely used in educational measurement and psychometrics, and the examinee’s aberrant responses will affect the estimation of their abilities. These examinees with aberrant responses should not be treated with conventional methods, the important thing is to accurately screen them out of the normal group. To achieve this, a common method is to construct person-fit statistics to detect whether the response patterns fit their estimated abilities.
In this study, a residual-based person-fit statistic R was proposed, which can be applied to both dichotomous or polytomous IRT models. The construction of R is based on a weighted residual between the observed response and the expected response. By accumulating the weighted residuals, the goodness of fit can be calculated and compared with a specific critical value to determine whether an examinee is aberrant or not. Given that tests with polytomous items can provide more information, polytomously scored items are being increasingly popular in educational measurement and psychometrics. The ability of R statistic to detect aberrant response patterns under the graded response model was mainly considered in this article.
An existing polytomous person-ft statistic lzp was also introduced in its outstanding standardized form and superior power. In the first study, a simulation study was conducted to generate the empirical distribution of R statistic and lzp. R statistic is an accumulation of weighted residuals, showing a positive skew distribution; lzp shows a negative skew distribution when the test is less than 80 items. Both of them differ from the standard normal distribution, It is necessary to set critical value according to the type 1 error, using it to distinguish whether each respondent's response pattern is fitted. In the second study, examinees with different aberrant behaviors (e.g., Cheaters, Lucky guessers, Random respondents, Careless respondents, Creative respondents and Mixed) under different test length conditions were simulated, and the detection rate as well as area under curve (AUC) were used to compare the effectiveness of the two person-fit statistics. The results show that the R statistic has a better detection rate than lzp when the aberrant behavior affects only a few items or the aberrant behavior is cheating or guessing. When the aberrant behavior covers plenty of items, lzp is slightly better than R statistic. Then, an empirical study was also conducted to show the power of R statistic.
Both of the R statistic and the lzp have their own pros and cons, so we may combine them in the future person-fit studies. The R statistic has a better detection rate under certain conditions compared to the lzp, especially when cheating and lucky guessing happened. Considering that cheating and guessing behaviors of low-ability examinees are more preferred in many aberrant test behaviors, the R statistic is worthy of further research and exploration in real-world applications.

Key words: polytomous items, item response theory, residual-based person-fit statistic, aberrant detection, polytomous item response models