Abstract: Cognitive diagnosis (CD), which is also referred as skill assessment or skill profiling, utilizes latent class models to provide fine-grained information about students’ strength and weakness in the learning process. One major advantage of CD is the capacity to provide additional information about the instructional needs of students. In the past decades, extensive research has been conducted in the area of CD and many statistical models based on a probabilistic approach have been proposed. Examples of cognitive diagnostic models (CDM) include the deterministic inputs, noisy and gate (DINA) model(Junker & Sijtsma, 2001), the deterministic input, noisy or gate (DINO) model (Templin & Henson, 2006), and C-RUM (Hartz, 2002). Currently, the outcome of CDM is a profile with binary element for each examine to indicate the mastery/non-mastery status of every attribute/skill, i.e. the attribute mastery status (AMS). But this coarse classification or diagnosis results unable to distinguish the individual differences between different students subtly, especially those students who are assigned into a same category. So the AMS may not conducive to be used by teachers to make decisions regarding the optimal intervention that should be put into place for the students. In order to obtain a nuanced profile of the student with respect to students’ characteristics, this study proposed the Probabilistic-Inputs, Noisy “And” gate (PINA) model based on the attribute mastery probability (AMP), which means that the AMP was used in CDM instead of the AMS. Firstly, model the AMP as arising from higher-order latent trait resembling the θ of item response models (de la Torre & Douglas, 2004). Then, the multicomponent latent traits model (Embretson, 1980, 1984) has been taken as a template from the PINA model. The results of a series of simulations based on Markov chain Monte Carlo methods showed that the model parameters and AMP-profiles can be recovered relatively accurately. An analysis of the fraction subtraction data is provided as an example. Key words□□cognitive diagnosis, attribute mastery probability, PINA model, higher-order latent traits, multicomponent latent traits

Key words: cognitive diagnosis, attribute mastery probability, PINA model, higher-order latent traits, multicomponent latent traits, item response theory, DINA

摘要： 当前认知诊断的主要目的是对被试进行合理分类，进而采用类别变量去描述被试对某技能或知识(即认知属性)的掌握情况，但该粗糙的分类方法不能精细地区分不同被试之间的差异。对此，采用掌握概率这一连续变量去描述被试对某认知属性的掌握情况是一种值得尝试的做法。本文首先基于高阶潜在特质(简称“潜质”)给出了认知属性掌握概率的量化定义，之后与多成分潜质模型相结合提出了概率性输入，噪音“与”门(PINA)模型；其次，采用MCMC算法实现了对PINA的参数估计，结果表明参数估计程序均对各参数的估计返真性均较好；最后，以“分数减法”数据为例来说明PINA在实际测验分析中具有可行性。

关键词: 认知诊断, 认知属性掌握概率, PINA, 高阶潜在特质, 多成分潜在特质, 项目反应理论, DINA