基于贝叶斯网的认知诊断模型构建

Bayesian Networks for Cognitive Diagnostic Modeling

新一代测量理论在测验设计、计量分析和结果解释等方面,都强调将认知科学与心理计量学相结合。文章基于贝叶斯网对定性的认知模型(属性层级)建立概率模型,并将其整合到认知诊断模型中,可实现认知模型与计量模型相结合进行诊断数据分析。采用MCMC算法分析带分数减法数据,比较不同属性结构下模型的表现,结果表明基于贝叶斯网构建的认知诊断模型可提供丰富且有效的诊断信息,可为验证认知模型提供一种途径。

With the coinciding developments in psychometrics and cognitive science in the past fifty years, more and more researchers are interested in combining these two fields to a new psychometric area, often called cognitively diagnostic assessment （CDA） （Fu ＆ Li, 2007）. How to incorporate these two fields into all aspects of development of CDA need future research to explore. The study only stems from viewing the mixing model between cognitive model and cognitive diagnostic model. The study considered the advantage and disadvantage among the attribute hierarchy method（AHM）, Bayesian networks model, deterministic inputs noisy and gate model（DINA） and reduced reparameterized unified model（R-RUM）. As Yan et al., （2004） saying, mixing the Bayesian network proficiency model with the fusion evidence model would produce a very attractive class of models. It allows the use of additional expert opinion in the proficiency model along with the fusion model statistics for item/skill correspondence. So we try to explore the mixing model and provide an analysis of fraction subtraction data as an example. In the analysis of fi-action subtraction data, two attribute hierarchies are considered, one （called AH1） only assumes that the attribute A3 is a prerequisite to attribute A4 and the other （called AH2） is derived from the Q-matrix the pairwise comparison method （Tatsuoka, 1995）. According to the augment algorithm, two reduced Q-matrices are obtained with 24 or 9 attribute patterns. Two Bayesian networks （called BN1 and BN2） corresponding to the above two attribute hierarchies are constructed according to the proficiency model （Yan, et al., 2004）, so two joint distributions of attribute pattern are specified, respectively. Under the above four attribute spaces, an independent attribute space （called AH0） and high-order proficiency model, the DINA model, the revised conjunctive DINA （R-DINA） model and the R-RUM are used to analyze Tatsuoka＇s fraction subtraction data using the Marker chain Monte Carlo （MCMC） algorithm. To compare these models under different attribute spaces, four relative fit statistics are considered in this study： -2log-likelihood （-2LL）, the Akaike＇s information criterion （AIC）, the Bayesian information criterion （BIC） （Chen et al., 2013） and deviance information criterion （DIC4, Celeux et al., 2006）.The results （see Table 1） indicate that： （a） The impact of different attribute spaces is very apparent： BNI and AH2 with similar results provide better than BN2, AH1 and AH0; BN2 and AH1 almost provide better than AH0. CO） The impact of three cognitive diagnosis models is also apparent, the R-RUM model outperform two others models with the R-DINA being slightly worse under all the conditions.（c）The results show some interaction effects between attribute space and cognitive diagnosis model. It is important to note that the impact of different attribute spaces on the R-RUM model is a relatively smaller than other models. Furthermore, by comparing the mean of skill estimate of the examinees with a total score of zero, the results （see Table 2） show that： For AH2, BN1 and BN2, examinees with a total score of zero are classified as not having all of the skills. However, for AH0 and AH1, the mean posterior probabilities of some skills is greater than .50.