Cognitive Diagnostic Assessment Based on Signal Detection Theory: Modeling and Application
Abstract: Cognitive diagnostic assessment (CDA) is aimed at diagnose which skills or attributes examinees have or do not have as the name expressed. This technique provides more useful feedback to examinees than a simple overall score got from classical test theory or item response theory. In CDA, multiple-choice (MC) is one of popular item types, which have the superiority on high test reliability, being easy to review, and scoring quickly and objectively. Traditionally, several cognitive diagnostic models (CDMs) have been developed to analyze the MC data by including the potential diagnostic information contained in the distractors.However, the response to MC items can be viewed as the process of extracting signals (correct options) from noises (distractors). Examinees are supposed to have perceptions of the plausibility of each options, and they make the decision based on the most plausible option. Meanwhile, there are two different states when examinee response to items: knows or does not know each item. Thus, the signal detection theory can be integrated into CDM to deal with MC data in CDA. The cognitive diagnostic model based on signal detection theory (SDT-CDM) is proposed in this paper and has several advantages over traditional CDMs. Firstly, it does not require the coding of q-vector for each option. Secondly, it provides discrimination and difficulty parameters that traditional CDMs cannot provide. Thirdly, it can directly express the relative differences between each options by plausibility parameters, providing a more comprehensive characterization of item quality.The results of two simulation studies showed that (1) the marginal maximum likelihood estimation approach via Expectation Maximization (MMLE/EM) algorithm could effectively estimate the model parameters of the SDT-CDM. (2) the SDT-CDM had high classification accuracy and parameter estimation precision, and could provide option-level information for item quality diagnosis. (3) independent variables such as the number of attributes, item quality, and sample size affected the performance of the SDT-CDM, but the overall results were promising. (4) compared with the nominal response diagnostic model (NRDM), the SDT-CDM was more accurate in classifying examinees under all data conditions.Further, an empirical study on the TIMSS 2011 mathematics assessment were conducted using both the SDT-CDM and the NRDM to inspect the ecological validity for the new model. The results showed that the SDT-CDM had better fitting and a smaller number of model parameters than the NRDM. The difficulty parameters of the SDT-CDM were significantly correlated with those of the two- (three-) parameter logical models. And the same was true of the discrimination parameters for the SDT-CDM. However, the correlation between the discrimination parameters of the NRDM and those of the two- (three-) parameter logical models was low and not significant. Besides, the classification accuracy and classification consistency of the SDT-CDM were higher than those of the NRDM. All the results indicated that the SDT-CDM was worth promoting.