Cognitive diagnostic assessment aims to measure specific knowledge structures in students. To model data arising from such assessments, cognitive diagnostic models with discrete latent variables have gained popularity in educational and behavioral sciences. In a learning context, the latent variables often denote sequentially acquired skill attributes, which is often modeled by the so-called attribute hierarchy method. One drawback of the traditional attribute hierarchy method is that its parameter complexity varies substantially with the hierarchy's graph structure, lacking statistical parsimony. Additionally, arrows among the attributes do not carry an interpretation of statistical dependence. Motivated by these, we propose a new family of latent conjunctive Bayesian networks (LCBNs), which rigorously unify the attribute hierarchy method for sequential skill mastery and the Bayesian network model in statistical machine learning. In an LCBN, the latent graph not only retains the hard constraints on skill prerequisites as an attribute hierarchy, but also encodes nice conditional independence interpretation as a Bayesian network. LCBNs are identifiable, interpretable, and parsimonious statistical tools to diagnose students' cognitive abilities from assessment data. We propose an efficient two-step EM algorithm for structure learning and parameter estimation in LCBNs. Application of our method to an international educational assessment dataset gives interpretable findings of cognitive diagnosis.

翻译：认知诊断评估旨在测量学生的具体知识结构。为对此类评估产生的数据进行建模，采用离散潜在变量的认知诊断模型已在教育科学和行为科学中广泛应用。在学习情境中，潜在变量常表示依次获得的技能属性，这通常通过所谓的属性层级方法进行建模。传统属性层级方法的一个缺陷在于，其参数复杂度随层级图结构显著变化，缺乏统计简洁性。此外，属性之间的箭头并不承载统计依赖性的解释意义。受此启发，我们提出了一类新的潜在合取贝叶斯网络（LCBNs），该方法严谨地统一了用于序列技能掌握的属性层级方法和统计机器学习中的贝叶斯网络模型。在LCBN中，潜在图不仅保留了属性层级中技能先决条件的硬性约束，还作为贝叶斯网络编码了良好的条件独立性解释。LCBNs是可识别、可解释且简洁的统计工具，可依据评估数据诊断学生的认知能力。我们提出了一种高效的两步EM算法，用于LCBN的结构学习和参数估计。将我们的方法应用于一项国际教育评估数据集，得到了可解释的认知诊断结果。