关键词: 认知诊断, 被试拟合, DINA 模型, 异常反应作答

Abstract: Cognitive Diagnostic Assessment (CDA) is a widely used educational assessment. It can provide guidance for further study and teaching by analyzing whether the test-takers have acquired knowledge points or skills.<br/>In psychometrics, statistical methods for assessing the fit of an examinee’s item responses to a postulated psychometric model are often called person-fit statistic. The person-fit analysis can help to verify diagnostic results, and is mainly used to distinguish the abnormal examinees from the normal ones. The abnormal response patterns include “sleeping” behavior, fatigue, cheating, creative responding, random guessing responses and cheating with randomness, all of which can affect the deviation of examinee’s ability estimation. The person-fit analysis can help researchers identify the abnormal response patterns more accurately, so as to delete the abnormal responding examinees and improve the validity of the test. In the past, most of the person fit researches were mainly carried out under the Item Response Theory (IRT) framework, while only few papers have been published dealing with person-fit under the CDM framework. This study attempts to fill a gap in the literature by introducing new methods. In this study, a new person fit index (R) was proposed. <br/>In order to verify the validity of the newly developed person fit index, this study explores the type I error and statistical test power of R index under different item length, item discrimination and different misfit types of respondent, and compares it with existing methods RCI and l_z. Type I error rate was defined as the proportion of flagged abnormal response patterns by a person fit statistic out of 1,000 generated normal response patterns from the DINA model. The control variables of this study include: the number of subjects is controlled to 1000, the cognitive diagnosis model is chosen as DINA model, the attributes are 6, and the Q matrix is fixed. Finally, to reflect the value of person fit index in practical application, the R index is applied to the empirical data of fractional subtraction. <br/>The results show that the type I error of R index is reasonable and stable at .05. In the aspect of statistical test power, with the improvement of item differentiation, the statistical test power of each index in different abnormal examinees is improved. With the increase in the number of items, most of the statistical power show an upward trend. For different types of abnormal subjects, R index perform best in the cases of random guessing responses and cheating with randomness. In the case of fatigue, sleep, and creative responding, the l_z index perform better. In the empirical data study, the detection rate of abnormal examinees is 4.29%.<br/>With the increase of the discrimination of items and the increase of the number of items, the power of R index has improved, and the performance of R index is the most robust when the discrimination of item is low. The R index has a high power for the types of abnormal behavior such as creative responding behavior, random guessing responses and cheating with randomness.

Key words: cognitive diagnosis, person fit, DINA model, aberrant response